Two-Qubit Geometric Phase Gate for Quantum Dot Spins using Cavity Polariton Resonance
Puri, Shruti; Yamamoto, Yoshihisa
2012-01-01
We describe a design to implement a two-qubit geometric phase gate, by which a pair of electrons confined in adjacent quantum dots are entangled. The entanglement is a result of the Coulomb exchange interaction between the optically excited exciton-polaritons and the localized spins. This optical coupling, resembling the electron-electron Ruderman-Kittel-Kasuya-Yosida (RKKY) inter- actions, offers high speed, high fidelity two-qubit gate operation with moderate cavity quality factor Q. The errors due to the finite lifetime of the polaritons can be minimized by optimizing the optical pulse parameters (duration and energy). The proposed design, using electrostatic quantum dots, maximizes entanglement and ensures scalability.
Exact two-qubit universal quantum circuit
Zhang, J; Sastry, S; Whaley, K B; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit gates. Each block in this circuit is given in a closed form solution. We also analyze the efficiency of different entangling gates, and find that exactly half of all the controlled-unitary gates can be used to implement two-qubit operations as efficiently as the commonly used CNOT gate.
Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED
Yang, Chui-Ping; Chu, Shih-I.; Han, Siyuan
2004-10-01
We propose a method for realizing two-qubit quantum phase gate with 4-level systems in cavity QED. In this proposal, the two logical states of a qubit are represented by the two lowest levels of each system, and two intermediate levels of each system are utilized to facilitate coherent control and manipulation of quantum states of the qubits. The present method does not involve cavity-photon population during the operation. In addition, we show that the gate can be achieved using only two-step operations.
Dynamical Suppression of Decoherence in Two-Qubit Quantum Memory
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, we have detailedly studied the dynamical suppression of the phase damping for the two-qubit quantum memory of Ising model by the quantum "bang-bang" technique. We find the sequence of periodic radiofrequency pulses repetitively to flip the state of the two-qubit system and quantitatively find that these pulses can be used to effectively suppress the phase damping decoherence of the quantum memory and freeze the system state into its initial state. The general sequence of periodic radio-frequency pulses to suppress the phase damping of multi-qubit of Ising model is also given.
Robust two-qubit quantum registers.
Grigorenko, I A; Khveshchenko, D V
2005-02-04
We carry out a systematic analysis of a pair of coupled qubits, each of which is subject to its own dissipative environment, and argue that a combination of the interqubit couplings which provides for the lowest possible decoherence rates corresponds to the incidence of a double spectral degeneracy in the two-qubit system. We support this general argument by the results of an evolutionary genetic algorithm which can also be used for optimizing time-dependent processes (gates) and their sequences that implement various quantum computing protocols.
Entanglement dynamics of two-qubit systems in different quantum noises
Institute of Scientific and Technical Information of China (English)
Pan Chang-Ning; Li-Fei; Fang Jian-Shu; Fang Mao-Fa
2011-01-01
The entanglement dynamics of two-qubit systems in different quantum noises are investigated by means of the operator-sum representation method. We find that, except for the amplitude damping and phase damping quantum noise, the sudden death of entanglement is always observed in different two-qubit systems with generalized amplitude damping and depolarizing quantum noise.
Minimum construction of two-qubit quantum operations
Zhang, J; Sastry, S; Whaley, K B; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. We also demonstrate that for the highly scalable Josephson junction charge qubits, the B gate is also more easily and quickly generated than the CNOT gate for physically feasible parameters.
Two-qubit quantum cloning machine and quantum correlation broadcasting
Kheirollahi, Azam; Mohammadi, Hamidreza; Akhtarshenas, Seyed Javad
2016-11-01
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: "Is there an optimal quantum cloning machine?" Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.
Extremal quantum correlations: Experimental study with two-qubit states
Energy Technology Data Exchange (ETDEWEB)
Chiuri, A.; Mataloni, P. [Dipartimento di Fisica, Sapienza Universita di Roma, Piazzale Aldo Moro 5, I-00185 Roma (Italy); Istituto Nazionale di Ottica (INO-CNR), L.go E. Fermi 6, I-50125 Firenze (Italy); Vallone, G. [Dipartimento di Fisica, Sapienza Universita di Roma, Piazzale Aldo Moro 5, I-00185 Roma (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89/A, Compendio del Viminale, I-00184 Roma (Italy); Paternostro, M. [Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queen' s University, Belfast BT7 1NN (United Kingdom)
2011-08-15
We explore experimentally the space of two-qubit quantum-correlated mixed states, including frontier states as defined by the use of quantum discord and von Neumann entropy. Our experimental setup is flexible enough to allow for high-quality generation of a vast variety of states. We address quantitatively the relation between quantum discord and a recently suggested alternative measure of quantum correlations.
Quantum discord for two-qubit X-states
Ali, Mazhar; Alber, Gernot
2010-01-01
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called X-states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they ar...
Quantum entanglement for two qubits in a nonstationary cavity
Berman, Oleg L.; Kezerashvili, Roman Ya.; Lozovik, Yurii E.
2016-11-01
The quantum entanglement and the probability of the dynamical Lamb effect for two qubits caused by nonadiabatic fast change of the boundary conditions are studied. The conditional concurrence of the qubits for each fixed number of created photons in a nonstationary cavity is obtained as a measure of the dynamical quantum entanglement due to the dynamical Lamb effect. We discuss the physical realization of the dynamical Lamb effect, based on superconducting qubits.
Quantum entanglement for two qubits in a nonstationary cavity
Berman, Oleg L; Lozovik, Yurii E
2016-01-01
The quantum entanglement and the probability of the dynamical Lamb effect for two qubits caused by non-adiabatic fast change of the boundary conditions are studied. The conditional concurrence of the qubits for each fixed number of created photons in a nonstationary cavity is obtained as a measure of the dynamical quantum entanglement due to the dynamical Lamb effect. We discuss the physical realization of the dynamical Lamb effect, based on superconducting qubits.
Application of quantum algorithms to direct measurement of concurrence of a two-qubit pure state
Institute of Scientific and Technical Information of China (English)
Wang Hong-Fu; Zhang Shou
2009-01-01
This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.
The two-qubit amplitude damping channel: Characterization using quantum stabilizer codes
Omkar, S.; Srikanth, R.; Banerjee, Subhashish; Shaji, Anil
2016-10-01
A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.
Joint remote state preparation (JRSP) of two-qubit equatorial state in quantum noisy channels
Adepoju, Adenike Grace; Falaye, Babatunde James; Sun, Guo-Hua; Camacho-Nieto, Oscar; Dong, Shi-Hai
2017-02-01
This letter reports the influence of noisy channels on JRSP of two-qubit equatorial state. We present a protocol for JRSP of two-qubit equatorial state. Afterward, we investigate the effects of five quantum noises on the protocol. We find that the system loses some of its properties as consequence of unwanted interactions with environment. For instance, within the domain 0 < λ < 0.65, the information lost via transmission of qubits in amplitude channel is most minimal, while for 0.65 < λ ≤ 1, the information lost in phase flip channel becomes the most minimal. Also, for any given λ, the information transmitted through depolarizing channel has the least chance of success.
A two-qubit photonic quantum processor and its application to solving systems of linear equations
Stefanie Barz; Ivan Kassal; Martin Ringbauer; Yannick Ole Lipp; Borivoje Dakić; Alán Aspuru-Guzik; Philip Walther
2014-01-01
Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, w...
Scheme for Remote Implementation of Partially Unknown Quantum Operation of Two Qubits in Cavity QED
Institute of Scientific and Technical Information of China (English)
QIU Liang; WANG An-Min
2008-01-01
By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits [An-Min Wang: Phys. Rev. A 74 (2006) 032317] with two-qubit Cnot gate and single qubit logic gates, we present a scheme to implement it in cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction between the atoms and the field of cavity is a nonresonant one. Finally, we analyze the experimental feasibility of this scheme.
One- and two-qubit logic using silicon-MOS quantum dots
Dzurak, Andrew
Spin qubits in silicon are excellent candidates for scalable quantum information processing due to their long coherence times and the enormous investment in silicon CMOS technology. While our Australian effort in Si QC has largely focused on spin qubits based upon phosphorus dopant atoms implanted in Si, we are also exploring spin qubits based on single electrons confined in SiMOS quantum dots. Such qubits can have long spin lifetimes T1 = 2 s, while electric field tuning of the conduction-band valley splitting removes problems due to spin-valley mixing. In isotopically enriched Si-28 these SiMOS qubits have a control fidelity of 99.6%, consistent with that required for fault-tolerant QC. By gate-voltage tuning the electron g*-factor, the ESR operation frequency can be Stark shifted by >10 MHz, allowing individual addressability of many qubits. Most recently we have coupled two SiMOS qubits to realize a CNOT gate using exchange-based controlled phase (CZ) operations. The speed of the two-qubit CZ-operations is controlled electrically via the detuning energy and over 100 two-qubit gates can be performed within a coherence time of 8 μs. We acknowledge support from the Australian Research Council (CE11E0001017), the US Army Research Office (W911NF-13-1-0024) and the Australian National Fabrication Facility.
A two-qubit photonic quantum processor and its application to solving systems of linear equations.
Barz, Stefanie; Kassal, Ivan; Ringbauer, Martin; Lipp, Yannick Ole; Dakić, Borivoje; Aspuru-Guzik, Alán; Walther, Philip
2014-08-19
Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations.
Novotny, J; Jex, I
2006-01-01
The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.
Institute of Scientific and Technical Information of China (English)
Wang Qiong; Li Ji-Xin; Zeng Hao-Sheng
2009-01-01
This paper investigates the change of entanglement for transmitting an arbitrarily entangled two-qubit pure state via one of three typical kinds of noisy quantum channels:amplitude damping quantum channel,phase damping quantum channel and depolarizing quantum channel.It finds,in all these three cases,that the output distant entanglement(measured by concurrence)reduces proportionately with respect to its initial amount,and the decaying ratio is determined only by the noisy characteristics of quantum channels and independent of the form of initial input state.
Two-Qubit Quantum Logic Gate in Molecular Magnets
Institute of Scientific and Technical Information of China (English)
HOU Jing-Min; TIAN Li-Jun; GE Mo-Lin
2005-01-01
@@ We propose a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled singlemolecule magnets, [Mn4]2. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between a pair of the four quantum computing bases and between the quantum computing bases and excited states are evaluated and analysed.
Controlled Remote Preparation of a Two-Qubit State via an Asymmetric Quantum Channel
Institute of Scientific and Technical Information of China (English)
WANG Zhang-Yin
2011-01-01
I present a new scheme for probabilistic remote preparation of a general two-qubit state from a sender to either of two receivers.The quantum channel is composed of a partial entangled tripartite Greenberger-Horne-Zeilinger (GHZ) state and a W-type state.I try to realize the remote two-qubit preparation by using the usual projective measurement and the method of positive operator-valued measure, respectively.The corresponding success probabilities of the scheme with different methods as well as the total classical communication cost required in this scheme are also calculated.
Quantum and classical correlations for a two-qubit X structure density matrix
Institute of Scientific and Technical Information of China (English)
Ding Bang-Fu; Wang Xiao-Yun; Zhao He-Ping
2011-01-01
We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix.Based on the characteristics of the expressions,the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method.We explain the relationships among quantum discord,classical correlation,and entanglement,and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state.The new method,which is different from previous approaches,has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state,such as a mixed state.
On the quantum discord of two-qubit X-states
Chen, Qing; Yu, Sixia; Yi, X X; Oh, C H
2011-01-01
Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X-states is proposed by Ali, Rau and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X-states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X-states for which their algorithm fails. And then we demonstrate that this special family of X-states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements.
Entanglement of Two-Qubit Quantum Heisenberg XYZ Chain
Institute of Scientific and Technical Information of China (English)
惠小强; 郝三如; 陈文学; 岳瑞宏
2002-01-01
We derive the analytic expression of the concurrence in the quantum Heisenberg XY Z model and discuss the influence of parameters J, △ and Γ on the concurrence. By choosing different values of Γ and △, we obtain the XX, XY, XXX and XXZ chains. The concurrence decreases with increasing temperature. When entanglement. For the XXZ chain, when Γ→∞, the concurence will meet its maximum value Cmax= sinh(1/T)--cosh(1/T)@
A practical scheme for quantum computation with any two-qubit entangling gate
Bremner, M J; Dodd, J L; Gilchrist, A; Harrow, A W; Mortimer, D; Nielsen, M A; Osborne, T J; Bremner, Michael J.; Dawson, Christopher M.; Dodd, Jennifer L.; Gilchrist, Alexei; Harrow, Aram W.; Mortimer, Duncan; Nielsen, Michael A.; Osborne, Tobias J.
2002-01-01
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].
Demonstrating quantum speed-up in a superconducting two-qubit processor
Dewes, A; Ong, F R; Schmitt, V; Milman, P; Bertet, P; Vion, D; Esteve, D
2011-01-01
We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover search algorithm among four objects and find that the correct answer is retrieved after a single run with a success probability between 0.52 and 0.67, significantly larger than the 0.25 achieved with a classical algorithm. This constitutes a proof-of-concept for the quantum speed-up of electrical quantum processors.
Conditional purity and quantum correlation measures in two qubit mixed states
Rebón, L.; Rossignoli, R.; Varga, J. J. M.; Gigena, N.; Canosa, N.; Iemmi, C.; Ledesma, S.
2016-11-01
We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.
Speed of quantum evolution of entangled two qubits states: Local vs. global evolution
Energy Technology Data Exchange (ETDEWEB)
Curilef, S [Departamento de Fisica, Universidad Catolica del Norte, Antofagasta (Chile); Zander, C; Plastino, A R [Physics Department, University of Pretoria, Pretoria 0002 (South Africa)], E-mail: arplastino@maple.up.ac.za
2008-11-01
There is a lower bound for the 'speed' of quantum evolution as measured by the time needed to reach an orthogonal state. We show that, for two-qubits systems, states saturating the quantum speed limit tend to exhibit a small amount of local evolution, as measured by the fidelity between the initial and final single qubit states after the time {tau} required by the composite system to reach an orthogonal state. Consequently, a trade-off between the speed of global evolution and the amount of local evolution seems to be at work.
Demonstration of two-qubit algorithms with a superconducting quantum processor.
DiCarlo, L; Chow, J M; Gambetta, J M; Bishop, Lev S; Johnson, B R; Schuster, D I; Majer, J; Blais, A; Frunzio, L; Girvin, S M; Schoelkopf, R J
2009-07-09
Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact-such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.
Towards optimizing two-qubit operations in three-electron double quantum dots
Frees, Adam; Gamble, John King; Mehl, Sebastian; Friesen, Mark; Coppersmith, S. N.
The successful implementation of single-qubit gates in the quantum dot hybrid qubit motivates our interest in developing a high fidelity two-qubit gate protocol. Recently, extensive work has been done to characterize the theoretical limitations and advantages in performing two-qubit operations at an operation point located in the charge transition region. Additionally, there is evidence to support that single-qubit gate fidelities improve while operating in the so-called ``far-detuned'' region, away from the charge transition. Here we explore the possibility of performing two-qubit gates in this region, considering the challenges and the benefits that may present themselves while implementing such an operational paradigm. This work was supported in part by ARO (W911NF-12-0607) (W911NF-12-R-0012), NSF (PHY-1104660), ONR (N00014-15-1-0029). The authors gratefully acknowledge support from the Sandia National Laboratories Truman Fellowship Program, which is funded by the Laboratory Directed Research and Development (LDRD) Program. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.
Indian Academy of Sciences (India)
Prasanta K Panigrahi; Siddharth Karumanchi; Sreraman Muralidharan
2009-09-01
We investigate the usefulness of the highly entangled five-partite cluster and Brown states for the quantum information splitting (QIS) of a special kind of two-qubit state using remote state preparation. In our schemes, the information that is to be shared is known to the sender. We show that, QIS can be accomplished with just two classical bits, as opposed to four classical bits, when the information that is to be shared is unknown to the sender. The present algorithm, demonstrated through the cluster and Brown states is deterministic as compared to the previous works in which it was probabilistic.
Erol, Volkan; Ozaydin, Fatih; Altintas, Azmi Ali
2014-06-24
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.
Hassan, Ali Saif M; Joag, Pramod S
2010-01-01
We investigate how thermal quantum discord $(QD)$ and classical correlations $(CC)$ of a two qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behaviour of $QD$ differs in many unexpected ways from thermal entanglement $(EN)$. For the nonuniform case, $(B_1= - B_2)$ we find that $QD$ and $CC$ are equal for all values of $(B_1=-B_2)$ and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which $QD$ and $CC$ are equal. The specification of this class and the corresponding conditions is completely general and apply to any quantum system in a state in this class and satisfying these conditions. We further find the relative contributions of $QD$ and $CC$ can be controlled easily by changing the relative magnitudes of $B_1$ and $B_2$.
Bartkiewicz, Karol; Chimczak, Grzegorz; Lemr, Karel
2017-02-01
We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of nine Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate both that these invariants are a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.
On Universal Gate Libraries and Generic Minimal Two-qubit Quantum Circuits
Shende, V V; Bullock, S S; Shende, Vivek V.; Markov, Igor L.; Bullock, Stephen S.
2003-01-01
We show how to implement exactly an arbitrary two-qubit unitary operation in several universal gate libraries using the smallest possible number of gates. To this end, we prove that n-qubit circuits using CNOT and one-qubit gates require at least ceil((4^n - 3n -1)/4) CNOT gates in the worst case. For two-qubit operators, this yields a lower bound of three gates, which we match with an upper bound of three gates. Using quantum circuit identities, we improve an earlier lower bound of 17 elementary gates by Bullock and Markov to 18, and their upper bound of 23 elementary gates to 18. We also improve upon the generic circuit with six CNOT gates by Zhang et al. (our circuit uses three), and that by Vidal and Dawson with 11 basic gates (we use 10). Given the available results, it appears that some universal gate libraries are at a disadvantage, at least in the sense that no construction is known to produce smallest possible circuits.
Dorai, Kavita; Arvind; Kumar, Anil
2001-01-01
We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search algorithm for two bits.
Quantum Dense Coding About a Two-Qubit Heisenberg XYZ Model
Xu, Hui-Yun; Yang, Guo-Hui
2017-09-01
By taking into account the nonuniform magnetic field, the quantum dense coding with thermal entangled states of a two-qubit anisotropic Heisenberg XYZ chain are investigated in detail. We mainly show the different properties about the dense coding capacity ( χ) with the changes of different parameters. It is found that dense coding capacity χ can be enhanced by decreasing the magnetic field B, the degree of inhomogeneity b and temperature T, or increasing the coupling constant along z-axis J z . In addition, we also find χ remains the stable value as the change of the anisotropy of the XY plane Δ in a certain temperature condition. Through studying different parameters effect on χ, it presents that we can properly turn the values of B, b, J z , Δ or adjust the temperature T to obtain a valid dense coding capacity ( χ satisfies χ > 1). Moreover, the temperature plays a key role in adjusting the value of dense coding capacity χ. The valid dense coding capacity could be always obtained in the lower temperature-limit case.
Yabu-uti, Bruno F C
2011-01-01
We propose an alternative scheme to implement a two-qubits Controlled-U gate in the hybrid system atom-$CCA$ (coupled cavities array). Our scheme results in a constant gating time and, with an adjustable qubit-bus coupling (atom-resonator), one can specify a particular transformation $U$ on the target qubit. We believe that this proposal may open promising perspectives for networking quantum information processors and implementing distributed and scalable quantum computation.
Energy Technology Data Exchange (ETDEWEB)
Yabu-uti, B.F.C., E-mail: yabuuti@ifi.unicamp.br [Instituto de Fisica ' Gleb Wataghin' , Universidade Estadual de Campinas, 13083-970 Campinas, SP (Brazil); Roversi, J.A., E-mail: roversi@ifi.unicamp.br [Instituto de Fisica ' Gleb Wataghin' , Universidade Estadual de Campinas, 13083-970 Campinas, SP (Brazil)
2011-08-22
We propose an alternative scheme to implement a two-qubit controlled-R (rotation) gate in the hybrid atom-CCA (coupled cavities array) system. Our scheme results in a constant gating time and, with an adjustable qubit-bus coupling (atom-resonator), one can specify a particular rotation R on the target qubit. We believe that this proposal may open promising perspectives for networking quantum information processors and implementing distributed and scalable quantum computation. -- Highlights: → We propose an alternative two-qubit controlled-rotation gate implementation. → Our gate is realized in a constant gating time for any rotation. → A particular rotation on the target qubit can be specified by an adjustable qubit-bus coupling. → Our proposal may open promising perspectives for implementing distributed and scalable quantum computation.
Energy Technology Data Exchange (ETDEWEB)
Hassan, Ali Saif M [Department of Physics, University of Amran, Amran (Yemen); Lari, Behzad; Joag, Pramod S, E-mail: alisaif73@gmail.co, E-mail: behzadlari1979@yahoo.co, E-mail: pramod@physics.unipune.ac.i [Department of Physics, University of Pune, Pune 411007 (India)
2010-12-03
We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case (B{sub 1} = -B{sub 2}), we find that QD and CC are equal for all values of (B{sub 1} = -B{sub 2}) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B{sub 1} and B{sub 2}. Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.
Institute of Scientific and Technical Information of China (English)
ZHANG Han; LUO Jun; REN Ting-Ting; SUN Xian-Ping
2010-01-01
@@ We report the experimental demonstration of decoherence dynamics of entanglement for the four Bell states in two-qubit nuclear-spin systems on ensemble quantum computers.Using artificial error operators to simulate noisy channels,we experimentally investigate the effect of noises on the four Bell states,and furthermore observe the time evolution of entanglement for the four Bell states in different noisy channels by calculating concurrences.Our experimental results show that the concurrences of the different Bell states under the same artificial error operations have the same values within the experimental error,and are independent of the different Bell states.These experimental results verify the theoretical evolution equation developed by Konrad et al.[Nature Phys.4 (2008) 99]for two-qubit entanglement.
Influence of Intrinsic Decoherence on Entanglement in Two-Qubit Quantum Heisenberg XYZ Chain
Institute of Scientific and Technical Information of China (English)
SHAO Bin; ZENG Tian-Hai; ZOU Jian
2005-01-01
Taking the intrinsic decoherence effect into account, we investigate the time evolution of entanglement for two-qubit XYZ Heisenberg model in an external uniform magnetic field. Concurrence, the measurement of entanglement,is calculated. We show how the intrinsic decoherence modifies the time evolution of the entanglement and find that at short-time case, concurrence is oscillating as increasing magnetic field, which implies that entanglement may be enhanced or weakened in some time regions.
Institute of Scientific and Technical Information of China (English)
秦涛; 高克林
2003-01-01
We propose a scheme to implement a two-qubit Grover quantum search algorithm.The novelty in the proposal is that the motional state is introduced into the computation and the internal state within a single cold trapped ion.The motional and internal states of the ion are manipulated as two qubits by the laser pulses to accomplish an example of a Grover algorithm based on the two qubits.The composite laser pulses that are applied to implement the Grover algorithm have been designed in detail.The issues concerning measurement and decoherence are discussed.
Sun, Wen-Yang; Wang, Dong; Shi, Jia-Dong; Ye, Liu
2017-02-01
In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a “sudden death” with increasing decoherence strength. However, shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while they initially share an entangled pure state, all EESs are steerable and obey Bell nonlocality in PF and phase damping channels. In BF channels, all steerable states can violate Bell-CHSH inequality, but some EESs are unable to be employed to realize steering. However, when they initially share an entangled mixed state, the outcome is different from that of the pure state. Furthermore, the steerability of entangled mixed states is weaker than that of entangled pure states. Thereby, decoherence can induce the degradation of quantum steering, and the steerability of state is associated with the interaction between quantum systems and reservoirs.
Sun, Wen-Yang; Wang, Dong; Shi, Jia-Dong; Ye, Liu
2017-01-01
In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a “sudden death” with increasing decoherence strength. However, shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while they initially share an entangled pure state, all EESs are steerable and obey Bell nonlocality in PF and phase damping channels. In BF channels, all steerable states can violate Bell-CHSH inequality, but some EESs are unable to be employed to realize steering. However, when they initially share an entangled mixed state, the outcome is different from that of the pure state. Furthermore, the steerability of entangled mixed states is weaker than that of entangled pure states. Thereby, decoherence can induce the degradation of quantum steering, and the steerability of state is associated with the interaction between quantum systems and reservoirs. PMID:28145467
Sirsi, Swarnamala; Hegde, Subramanya
2011-01-01
Quantum computation on qubits can be carried out by an operation generated by a Hamiltonian such as application of a pulse as in NMR, NQR. Quantum circuits form an integral part of quan- tum computation. We investigate the nonlocal operations generated by a given Hamiltonian. We construct and study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power. Our work addresses the problem of analyzing the quantum evolution in the special case of two qubit symmetric states. Such a symmetric space can be considered to be spanned by the angular momentum states {|j = 1,m>;m = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of newly defined Hermitian operators Mk's (k= 0.....8) which are constructed out of angular momentum operators Jx, Jy, Jz. These operators constitute a linearly independent set of traceless matrices (except for M0). Further...
Quantum state tomography for quadrupole nuclei and its applications on a two-qubit system
Energy Technology Data Exchange (ETDEWEB)
Bonk, F.A.; Azevedo, E.R. de; Mantovani, G.L.; Bonagamba, T.J. [Sao Paulo Univ., Sao Carlos, SP (Brazil). Inst. de Fisica]. E-mail: azevedo@if.sc.usp.br; Sarthour, R.S.; Bulnes, J.D.; Guimaraes, A.P.; Oliveira, I.S. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mails: sarthour@cbpf.br; apguima@cbpf.br; ivan@cbpf.br; Freitas, J.C.C. [Espirito Santo Univ., Vitoria (Brazil). Dept. de Fisica
2004-05-01
A method for performing quantum state tomography for quadrupole nuclei is presented in this paper. First, it is shown that upon appropriate phase cycling, the NMR intensities of quadrupole nuclei depend only on diagonal elements of the density matrix. Thus, a method for obtaining the density matrix elements, which consists of dragging off-diagonal elements into the main diagonal using fine phase-controlled selective radiofrequency pulses, was derived. The use of the method is exemplified through {sup 23} Na NMR (nuclear spin I = 3/2) in a lyotropic liquid-crystal at room temperature, in three applications: (a) the tomography of pseudo-pure states; (b) the tomography of the quadrupole free evolution of the density matrix, and (c) the unitary state evolution of each qubit in the system over the Bloch sphere upon the application of a Hadamard gate. Further applications in the context of pure NMR and in the context of quantum information processing, as well as generalizations for higher spins, are discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Kato, Akihito, E-mail: kato@kuchem.kyoto-u.ac.jp; Tanimura, Yoshitaka, E-mail: tanimura@kuchem.kyoto-u.ac.jp [Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan)
2015-08-14
We consider a system consisting of two interacting qubits that are individually coupled to separate heat baths at different temperatures. The quantum effects in heat transport are investigated in a numerically rigorous manner with a hierarchial equations of motion (HEOM) approach for non-perturbative and non-Markovian system-bath coupling cases under non-equilibrium steady-state conditions. For a weak interqubit interaction, the total system is regarded as two individually thermostatted systems, whereas for a strong interqubit interaction, the two-qubit system is regarded as a single system coupled to two baths. The roles of quantum coherence (or entanglement) between the two qubits (q-q coherence) and between the qubit and bath (q-b coherence) are studied through the heat current calculated for various strengths of the system-bath coupling and interqubit coupling for high and low temperatures. The same current is also studied using the time convolutionless (TCL) Redfield equation and using an expression derived from the Fermi golden rule (FGR). We find that the HEOM results exhibit turnover behavior of the heat current as a function of the system-bath coupling strength for all values of the interqubit coupling strength, while the results obtained with the TCL and FGR approaches do not exhibit such behavior, because they do not possess the capability of treating the q-b and q-q coherences. The maximum current is obtained in the case that the q-q coherence and q-b coherence are balanced in such a manner that coherence of the entire heat transport process is realized. We also find that the heat current does not follow Fourier’s law when the temperature difference is very large, due to the non-perturbative system-bath interactions.
Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field
Li, Lei; Yang, Guo-Hui
2014-07-01
Quantum correlations in an anisotropic Heisenberg XYZ chain is investigated by use of concurrence C and measurement-induced disturbance (MID). We show that the behaviors of the MID are remarkably different from the concurrence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures, we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant Jz, while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter γ, whereas an opposite effect for MID behaviors is presented.
Teleportation-based realization of an optical quantum two-qubit entangling gate
Gao, Wei-Bo; Lu, Chao-Yang; Dai, Han-Ning; Wagenknecht, Claudia; Zhang, Qiang; Zhao, Bo; Peng, Cheng-Zhi; Chen, Zeng-Bing; Chen, Yu-Ao; Pan, Jian-Wei
2010-01-01
In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by Gottesman and Chuang [Nature \\textbf{402}, 390 (1999)], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multi-particle entangled states, Bell state measurements and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods we demonstrate the smallest non-trivial module in such a scheme---a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-...
Liu, Tang-Kun; Tao, Yu; Shan, Chuan-Jia; Liu, Ji-bing
2017-10-01
Using the three criterions of the concurrence, the negative eigenvalue and the geometric quantum discord, we investigate the quantum entanglement and quantum correlation dynamics of two two-level atoms interacting with the coherent state optical field. We discuss the influence of different photon number of the mean square fluctuations on the temporal evolution of the concurrence, the negative eigenvalue and the geometric quantum discord between two atoms when the two atoms are initially in specific three states. The results show that different photon number of the mean square fluctuations can lead to different effects of quantum entanglement and quantum correlation dynamics.
Liu, Tang-Kun; Tao, Yu; Shan, Chuan-Jia; Liu, Ji-bing
2017-08-01
Using the three criterions of the concurrence, the negative eigenvalue and the geometric quantum discord, we investigate the quantum entanglement and quantum correlation dynamics of two two-level atoms interacting with the coherent state optical field. We discuss the influence of different photon number of the mean square fluctuations on the temporal evolution of the concurrence, the negative eigenvalue and the geometric quantum discord between two atoms when the two atoms are initially in specific three states. The results show that different photon number of the mean square fluctuations can lead to different effects of quantum entanglement and quantum correlation dynamics.
Classical Emulation of a Two-Qubit Quantum Computer with Analog Electronics
La Cour, Brian; Ostrove, Corey; Ott, Granville; Starkey, Michael; Wilson, Gary
Abstract: The Hilbert space mathematical structure of a gate-based quantum computer may be reproduced by mapping the computational basis states to corresponding functions in the space of complex exponentials and identifying an inner product between any two such functions. The span of these complex basis exponentials may then identified with the finite-dimensional Hilbert space of a gate-based quantum computer. By using classical analog electronic components, such as four-quadrant multipliers and operational amplifiers, voltage signals representing arbitrary four-dimensional quantum states, along with the equivalent gate and measurement operations of a quantum computer have been physically realized through the corresponding circuitry. The fidelity of the emulation is measured using both a direct evaluation of the signal as well as through an emulation of quantum state tomography to infer the quantum state. We demonstrate that for both state synthesis and gate operations, our quantum emulation device is capable of achieving over 99% fidelity. This work was supported by the Office of Naval Research under Grant No. N00014-14-1-0323.
Investigations of the Quantum Correlation in Two-Qubit Heisenberg XYZ Model with Decoherence
Guo-Hui, Yang
2016-12-01
Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated with the use of concurrence C and quantum discord (QD). With the Werner state as the initial state, we discuss the influence of mixture degree r on the dynamics. There are some difference between the time evolution behaviors of these two correlation measures with different value of r. For 0 ≤ r ≤ 1/3, there exists quantum discord but no entanglement; For 1/3
Two qubits in the Dirac representation
Rajagopal, A. K.; Rendell, R. W.
2001-08-01
The Dirac-matrix representation of a general two-qubit system is shown to exhibit quite interesting features. The relativistic symmetries of time reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the Bell states. It is shown that only C does not mix the Bell states whereas all others do. The various logic gates of quantum information theory are also expressed in terms of the Dirac matrices. For example, the NOT gate is related to the product of T and P. A two-qubit density matrix is found to be entangled if it is invariant under C.
Two-qubit correlations via a periodic plasmonic nanostructure
Energy Technology Data Exchange (ETDEWEB)
Iliopoulos, Nikos; Terzis, Andreas F. [Department of Physics, School of Natural Sciences, University of Patras, Patras 265 04 (Greece); Yannopapas, Vassilios [Department of Physics, National Technical University of Athens, Athens 157 80 (Greece); Paspalakis, Emmanuel, E-mail: paspalak@upatras.gr [Materials Science Department, School of Natural Sciences, University of Patras, Patras 265 04 (Greece)
2016-02-15
We theoretically investigate the generation of quantum correlations by using two distant qubits in free space or mediated by a plasmonic nanostructure. We report both entanglement of formation as well as quantum discord and classical correlations. We have found that for proper initial state of the two-qubit system and distance between the two qubits we can produce quantum correlations taking significant value for a relatively large time interval so that it can be useful in quantum information and computation processes.
Quantum gates with topological phases
Ionicioiu, R
2003-01-01
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.
McCloskey, R.; Ferraro, A.; Paternostro, M.
2017-01-01
We identify the families of states that maximize some recently proposed quantifiers of Einstein-Podolsky-Rosen (EPR) steering and the volume of the quantum steering ellipsoid (QSE). The optimal measurements which maximize genuine EPR steering measures are discussed and we develop a way to find them using the QSE. We thus explore the links between genuine EPR steering and the QSE and introduce states that can be the most useful for one-sided device-independent quantum cryptography for a given amount of noise.
Singh, Manu Pratap; Rajput, B. S.
2016-03-01
Recall operations of quantum associative memory (QuAM) have been conducted separately through evolutionary as well as non-evolutionary processes in terms of unitary and non- unitary operators respectively by separately choosing our recently derived maximally entangled states (Singh-Rajput MES) and Bell's MES as memory states for various queries and it has been shown that in each case the choices of Singh-Rajput MES as valid memory states are much more suitable than those of Bell's MES. it has been demonstrated that in both the types of recall processes the first and the fourth states of Singh-Rajput MES are most suitable choices as memory states for the queries `11' and `00' respectively while none of the Bell's MES is a suitable choice as valid memory state in these recall processes. It has been demonstrated that all the four states of Singh-Rajput MES are suitable choice as valid memory states for the queries `1?', `?1', `?0' and `0?' while none of the Bell's MES is suitable choice as the valid memory state for these queries also.
Optimal copying of entangled two-qubit states
Novotny, J; Jex, I
2004-01-01
We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect to two separable copies. These optimal copying processes hint at the intricate relationship between fundamental laws of quantum theory and entanglement.
System-environment correlations for dephasing two-qubit states coupled to thermal baths
Costa, A. C. S.; Beims, M. W.; Strunz, W. T.
2016-05-01
Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial X state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature Tcrit. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to Tcrit the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.
Effects of Noise on Joint Remote State Preparation of an Arbitrary Equatorial Two-Qubit State
Zhao, Hong-xia; Huang, Li
2017-03-01
By using a six-qubit cluster state as the quantum channel, we investigat the joint remote state preparation of an arbitrary equatorial two-qubit state. We analytically obtain the fidelities of the joint remote state preparation process in noisy environments, such as the amplitude-damping noise and phase-damping noise. In our scheme, the two different noise including amplitude-damping noise and the phase-damping noise only affect the travel qubits of the quantum channel, and then we show that the fidelities in these two noisy cases only depend on the decoherence noisy rate.
Enhancing the fidelity of two-qubit gates by measurements
Gefen, Tuvia; Cohen, Daniel; Cohen, Itsik; Retzker, Alex
2017-03-01
Dynamical decoupling techniques are the method of choice for increasing gate fidelities. While these methods have produced very impressive results in terms of decreasing local noise and increasing the fidelities of single-qubit operations, dealing with the noise of two-qubit gates has proven more challenging. The main obstacle is that the noise time scale is shorter than the two-qubit gate itself, so that refocusing methods do not work. We present a measurement- and feedback-based method to suppress two-qubit-gate noise, which cannot be suppressed by conventional methods. We analyze in detail this method for an error model, which is relevant for trapped-ion quantum information.
Two Qubits in the Dirac Representation
Rajagopal, A K
2000-01-01
A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states under these symmetry operations also reveal that C is the only operator that does not mix the Bell states whereas all others do. In a similar fashion, expressing the various logic gates introduced in the subject of quantum computers in terms of the Dirac matrices shows for example, that the NOT gate is related to the product of time-reversal and parity operators.
Projective Ring Line Encompassing Two-Qubits
Saniga, M; Pracna, P; Planat, Michel; Pracna, Petr; Saniga, Metod
2006-01-01
The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF(2) is found to fully accommodate the algebra of 15 operators -- generalized Pauli matrices -- characterizing two-qubit systems. The relevant sub-configuration consits of 15 points each of which is either simultaneusly distant or simultaneously neighbour to (any) two given distant points of the line. The operators can be identified with the points in such a one-to-one manner that their commutation relations are exactly reproduced by the underlying geometry of the points, with the ring geometrical notions of neighbour/distant answering, respectively, to the operational ones of commuting/non-commuting. This finding opens up rather unexpected vistas for an algebraic geometrical modelling of finite-dimensional quantum systems and gives their numerous applications a wholy new perspective.
Controlled phase gates based on two nonidentical quantum dots trapped in separate cavities
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Xia; Zhang Jian-Qi; Yu Ya-Fei; Zhang Zhi-Ming
2011-01-01
We propose a scheme for realizing two-qubit controlled phase gates on two nonidentical quantum dots trapped in separate cavities.In our scheme,each dot simultaneously interacts with one highly detuned cavity mode and two strong driven classical fields.During the gate operation,the quantum dots undergo no transition,while the system can acquire different phases conditional on different states of the quantum dots.With the application of the single-qubit operations,two-qubit controlled phase gates can be realized.
Recognizing Small-Circuit Structure in Two-Qubit Operators
Shende, V V; Markov, I L; Shende, Vivek V.; Bullock, Stephen S.; Markov, Igor L.
2003-01-01
This work describes numerical tests which determine whether a two-qubit quantum computation has an atypically simple quantum circuit. Specifically, we describe forumulae, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-not gates with all other gates being local unitary. Circuit diagrams are provided in each case. We expect significant impact in physical implementations where controlled-not's are more difficult than one-qubit computations. Our results can be contrasted with those by Zhang et al., Bullock and Markov, Vidal and Dawson, and Shende et al. In these works, small quantum circuits are achieved for arbitrary two-qubit operators, and the latter two prove three controlled-not's suffice. However, unitary operators with the sort of structure described above may not be detected. Our work provides results similar to those by Song and Klappenecker but for a wider range of operators.
Effect of noise on deterministic joint remote preparation of an arbitrary two-qubit state
Wang, Ming-Ming; Qu, Zhi-Guo; Wang, Wei; Chen, Jin-Guang
2017-05-01
Quantum communication has attracted much attention in recent years. Deterministic joint remote state preparation (DJRSP) is an important branch of quantum secure communication which could securely transmit a quantum state with 100% success probability. In this paper, we study DJRSP of an arbitrary two-qubit state in noisy environment. Taking a GHZ based DJRSP scheme of a two-qubit state as an example, we study how the scheme is influenced by all types of noise usually encountered in real-world implementations of quantum communication protocols, i.e., the bit-flip, phase-flip (phase-damping), depolarizing, and amplitude-damping noise. We demonstrate that there are four different output states in the amplitude-damping noise, while there is the same output state in each of the other three types of noise. The state-independent average fidelity is presented to measure the effect of noise, and it is shown that the depolarizing noise has the worst effect on the DJRSP scheme, while the amplitude-damping noise or the phase-flip has the slightest effect depending on the noise rate. Our results are also suitable for JRSP and RSP.
Entangled Bloch Spheres: Bloch Matrix And Two Qubit State Space
Gamel, Omar
2016-01-01
We represent a two qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parameterize and visualize the two qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch spheres with superimposed correlation axes. It is shown that unitary transformations, local or nonlocal, have simple interpretations as axis rotations or mixing of certain degrees of freedom. The nonlocal unitary invariants of the state are then derived in terms of local unitary invariants. The positive partial transpose criterion for entanglement is generalized, and interpreted as a reflection, or a change of a single ...
Two qubits of a W state violate Bell's inequality beyond Cirel'son's bound
Cabello, A
2002-01-01
It is shown that the correlations between two qubits selected from a trio prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more than the correlations between two qubits in any quantum state. Such a violation beyond Cirel'son's bound is smaller than the one achieved by two qubits selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local observers can know from their own measurements whether their qubits belongs or not to the selected pair.
Wang, Hao; Wu, Guoxing; Chen, Daojiong
2012-07-01
Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii-Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.
Energy Technology Data Exchange (ETDEWEB)
Akibue, Seiseki [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo (Japan); Murao, Mio [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan and NanoQuine, The University of Tokyo, Tokyo (Japan)
2014-12-04
We investigate distributed implementation of two-qubit unitary operations over two primitive networks, the butterfly network and the ladder network, as a first step to apply network coding for quantum computation. By classifying two-qubit unitary operations in terms of the Kraus-Cirac number, the number of non-zero parameters describing the global part of two-qubit unitary operations, we analyze which class of two-qubit unitary operations is implementable over these networks with free classical communication. For the butterfly network, we show that two classes of two-qubit unitary operations, which contain all Clifford, controlled-unitary and matchgate operations, are implementable over the network. For the ladder network, we show that two-qubit unitary operations are implementable over the network if and only if their Kraus-Cirac number do not exceed the number of the bridges of the ladder.
Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit Entangled State
Institute of Scientific and Technical Information of China (English)
FANG Ming; LIU Yi-Min; LIU Jun; SHI Shou-Hua; ZHANG Zhan-Jun
2006-01-01
Based on A.K. Pati's original idea [Phys. Rev. A 61 (2000) 022308] on single-qubit-state-assisted clone, very recently Zhan has proposed two assisted quantum cloning protocols of a special class of unknown two-qubit entangled states [Phys. Lett. A 336 (2005) 317]. In this paper we further generalize Zhan's protocols such that an arbitrary unknown two-qubit entangled state can be treated.
Adiabatic phase-conserving processes for executing quantum operations with ultracold atoms
Beterov, I. I.; Tret'yakov, D. B.; Entin, V. M.; Yakshina, E. A.; Khamzina, G. N.; Ryabtsev, I. I.
2017-06-01
We have studied the regimes of deterministic single-atom Rydberg excitation in the conditions of Rydberg blockade and the methods of compensation for the dynamic phase of the wave function during the adiabatic passage. Using these methods, we have proposed schemes of single-qubit and two-qubit quantum states with mesoscopic atomic ensembles containing a random number of atoms, considred as quibits. The double adiabatic passage of the Förster resonance for two interacting atoms with a deterministic phase shift can be used for the implementation of two-qubit gates with reduced sensitivity of the gate fidelity to the fluctuations of the interatomic distance.
Systematically Generated Two-Qubit Braids for Fibonacci Anyons
Zeuch, Daniel; Carnahan, Caitlin; Bonesteel, N. E.
We show how two-qubit Fibonacci anyon braids can be generated using a simple iterative procedure which, in contrast to previous methods, does not require brute force search. Our construction is closely related to that of, but with the new feature that it can be used for three-anyon qubits as well as four-anyon qubits. The iterative procedure we use, which was introduced by Reichardt, generates sequences of three-anyon weaves that asymptotically conserve the total charge of two of the three anyons, without control over the corresponding phase factors. The resulting two-qubit gates are independent of these factors and their length grows as log 1/ ɛ, where ɛ is the error, which is asymptotically better than the Solovay-Kitaev method.
A scheme for conditional quantum phase gate via bimodal cavity and a Λ-type three-level atom
Institute of Scientific and Technical Information of China (English)
Cai Jian-Wu; Fang Mao-Fa; Liao Xiang-Ping; Zheng Xiao-Juan
2006-01-01
We propose a scheme to implement a two-qubit conditional quantum phase gate for the intracavity field via a single three-level Λ-type atom driven by two modes in a high-Q cavity. The quantum information is encoded on the Fock states of the bimodal cavity. The gate's averaged fidelity is expected to reach 99.8%.
One step to generate quantum controlled phase-shift gate using a trapped ion
Institute of Scientific and Technical Information of China (English)
Zhang Shi-Jun; Ma Chi; Zhang Wen-Hai; Ye Liu
2008-01-01
This paper presents a very simple scheme for generating quantum controlled phase-shift gate with only one step by using the two vibrational modes of a trapped ion as the two qubits.The scheme couples two vibration degrees of freedom coupled with a suitable chosen laser excitation via the ionic states.
Engineering extremal two-qubit entangled states with maximally entangled Gaussian light
Adesso, G; Illuminati, F; Paternostro, M
2010-01-01
We study state engineering induced by bilinear interactions between two remote qubits and light fields prepared in two-mode Gaussian states. The attainable two-qubit states span the entire physically allowed region in the entanglement-vs-global-purity plane. We show that two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. The target two-qubit entanglement is determined quantitatively only by the purities of the two-mode Gaussian resource. Thus, a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control completely the engineering of extremally entangled two-qubit states, which can be realized in realistic scenarios of cavity and circuit quantum electrodynamics.
Entanglement Dynamics of Two Qubits Coupled to a Noise Environmen
Institute of Scientific and Technical Information of China (English)
LIU Jin; XIANG Shao-Hua; CUI Hui-Ping; LI Jian
2009-01-01
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise.It is shown that due to environment noise, all quantum entangled states axe very fragile and become a classical mixed state in a short-time limit.But the environment can affect entanglement in very different ways.The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
Note on Entanglement of an Arbitrary State of Two Qubits
Institute of Scientific and Technical Information of China (English)
WANG An-Min
2000-01-01
It is shown that the norm of the polarization vector of the reduced density matrix can characterize the entangle ment of two qubits and so it is defined as a simple measure of entanglement. It is then extended to the generalized entanglement of polarization vector. It is proved that the entanglement of formation belongs to the generalized entanglement of polarization vector. Under the local general measurement and classical communication how this generalized entanglement of polarization vector changes is proved strictly and so the first and second laws of quantum information processing are verified clearly.
Unconventional geometric quantum phase gates with a cavity QED system
Zheng, Shi-Biao
2004-11-01
We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.
Tomographic causal analysis of two-qubit states and tomographic discord
Energy Technology Data Exchange (ETDEWEB)
Kiktenko, Evgeny [Bauman Moscow State Technical University, 2nd Baumanskaya St., 5, Moscow 105005 (Russian Federation); Geoelectromagnetic Research Center of Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, PO Box 30, Troitsk, Moscow Region 142190 (Russian Federation); Fedorov, Aleksey, E-mail: akf@rqc.ru [Bauman Moscow State Technical University, 2nd Baumanskaya St., 5, Moscow 105005 (Russian Federation); Russian Quantum Center, Novaya St. 100, Skolkovo, Moscow 143025 (Russian Federation)
2014-05-01
We study a behavior of two-qubit states subject to tomographic measurement. In this Letter we propose a novel approach to definition of asymmetry in quantum bipartite state based on its tomographic Shannon entropies. We consider two types of measurement bases: the first is one that diagonalizes density matrices of subsystems and is used in a definition of tomographic discord, and the second is one that maximizes Shannon mutual information and relates to symmetrical form quantum discord. We show how these approaches relate to each other and then implement them to the different classes of two-qubit states. Consequently, new subclasses of X-states are revealed.
Relative Entropy of Entanglement of One Class of Two-Qubit System
Institute of Scientific and Technical Information of China (English)
LIANG Lin-Mei; CHEN Ping-Xing; LI Cheng-Zu; HUANG Ming-Qiu
2001-01-01
The relative entropy of entanglement of a mixed state σ for a bipartite quantum system can be defined as the minimum of the quantum relative entropy over the set of completely disentangled states. Vedral et al. [Phys.Rev. A 57(1998)1619] have recently proposed a numerical method to obtain the relative entropy of entanglement Ere for two-qubit systems. This letter shows that the convex programming method can be applied to calculate Ere of two-qubit systems analytically, and discusses the conditions under which the method can be adopted.
Luo, Xiao-Qing; Fan, Heng; Liu, Wu-Ming
2012-01-01
We investigate the linear and nonlinear properties of the probe and signal optical pulses based on intersubband transitions in an asymmetric GaAs/AlGaAs double quantum wells. It shows that, in the presence of cross-phase modulation, a giant cross-Kerr nonlinearity and mutually matched group velocities of the probe and signal optical pulses can be achieved while realizing the suppression of linear and self-Kerr optical absorption synchronously. These characteristics serve to exhibit an all-optical two-qubit polarization controlled quantum phase gate within efficiently controllable photon-photon entanglement by semiconductor mediation. In addition, by using just polarizing beam and half-wave plates, we propose a practical experimental scheme to discriminate the maximally entangled polarization state of two-qubit through distinguishing two out of the four Bell states. This proposal potentially enables the realization of solid states mediated all-optical quantum computation and information processing.
The Veldkamp Space of Two-Qubits
Directory of Open Access Journals (Sweden)
Metod Saniga
2007-06-01
Full Text Available Given a remarkable representation of the generalized Pauli operators of two-qubits in terms of the points of the generalized quadrangle of order two, W(2, it is shown that specific subsets of these operators can also be associated with the points and lines of the four-dimensional projective space over the Galois field with two elements - the so-called Veldkamp space of W(2. An intriguing novelty is the recognition of (uni- and tri-centric triads and specific pentads of the Pauli operators in addition to the ''classical'' subsets answering to geometric hyperplanes of W(2.
Concurrence Measurement for the Two-Qubit Optical and Atomic States
Directory of Open Access Journals (Sweden)
Lan Zhou
2015-06-01
Full Text Available Concurrence provides us an effective approach to quantify entanglement, which is quite important in quantum information processing applications. In the paper, we mainly review some direct concurrence measurement protocols of the two-qubit optical or atomic system. We first introduce the concept of concurrence for a two-qubit system. Second, we explain the approaches of the concurrence measurement in both a linear and a nonlinear optical system. Third, we introduce some protocols for measuring the concurrence of the atomic entanglement system.
Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain
Institute of Scientific and Technical Information of China (English)
QIN Meng; TAO Ying-Juan; TIAN Dong-Ping
2008-01-01
We investigate quantum teleportation as a tool to study the thermally entangled state of a twoqubit Heisenberg XXZ chain.Our work is mainly to investigate the characteristics of a Heisenberg XXZ chain and get some analytical results of the fully entangled fraction.We also consider the entanglement teleportation via a two-qubit Heisenberg XXZ chain.
Intrinsic Decoherence on Two-Qubit Heisenberg ⅩⅩ Chain
Institute of Scientific and Technical Information of China (English)
HE Zheng-Hong; XIONG Zu-Hong; HU Dong-Mei
2007-01-01
Quantum teleportation is investigated by using the entangled states of two-qubit Heisenberg ⅩⅩ chain in an external uniform magnetic field as resources in the model of Milburn's intrinsic decoherence. Though intrinsic decoherence on quantum entanglement and quantum teleportation exerts different effects in different initial systems,proper magnetic fields and probabilities of different eigenstates in the initial states can weaken the effects.
Optimal two qubit gate for generation of random bipartite entanglement
Znidaric, M
2007-01-01
We study protocols for generation of random pure states consisting of repeated applications of two qubit transformations. Necessary number of steps needed in order to generate states displaying bipartite entanglement typical of random states is obtained. We also find the optimal two qubit gate for which the convergence is the fastest. Perhaps surprisingly, applying the same good two qubit gate in addition to a random single qubit rotations at each step leads to a faster generation of entanglement than applying a random two qubit transformation at each step.
Efficient controlled-phase gate for single-spin qubits in quantum dots
Meunier, T.; Calado, V.E.; Vandersypen, L.M.K.
2011-01-01
Two-qubit interactions are at the heart of quantum information processing. For single-spin qubits in semiconductor quantum dots, the exchange gate has always been considered the natural two-qubit gate. The recent integration of a magnetic field or g-factor gradients in coupled quantum dot systems
Directory of Open Access Journals (Sweden)
R Afzali
2013-03-01
Full Text Available Because the key issue in quantum information and quantum computing is entanglement, the investigation of the effects of environment, as a source of quantum dissipation, and interaction between environment and system on entanglement and quantum phase transition is important. In this paper, we consider two-qubit system in the anisotropic Heisenberg XXZ model with the Dzyaloshinskii-moriya interaction, and accompanied quantum dissipation. Using Lindblad dynamics, the coupling effect and also temperature effect on concurrence, as a measure of entanglement of system, is obtained. The role of DM interaction parameters in the evolution of entanglement is investigated. Furthermore, using derivative of concurrence, the effects of dissipation and DM interaction parameter on quantum phase transition are obtained. It should be noted that spin-orbit interaction or DM parameter intensively influence the process of impressments of dissipation on entanglement measure and quantum phase transition. The current research is very important in the topics of nanometric systems.
Cavity QED quantum phase gates for a single longitudinal mode of the intracavity field
García-Maraver, R; Eckert, K; Rebic, S; Artoni, M; Mompart, J
2004-01-01
A single three-level atom driven by a longitudinal mode of a high-Q cavity is used to implement two-qubit quantum phase gates for the intracavity field. The two qubits are associated to the zero-and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom yields the conditional phase gate provided the two polarization states and the atom interact in a $V$-type configuration and the two photon resonance condition is fulfilled. Microwave and optical implementations are discussed with gate fidelities being evaluated against several decoherence mechanisms such as atomic velocity fluctuations or the presence of a weak magnetic field. The use of coherent states for both polarization states is investigated to assess the entanglement capability of the proposed quantum gates.
Cavity QED quantum phase gates for a single longitudinal mode of the intracavity field
García-Maraver, R.; Corbalán, R.; Eckert, K.; Rebić, S.; Artoni, M.; Mompart, J.
2004-12-01
A single three-level atom driven by a longitudinal mode of a high- Q cavity is used to implement two-qubit quantum phase gates for the intracavity field. The two qubits are associated with the zero- and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom mediates the conditional phase gate provided the two polarization states and the atom interact in a V-type configuration and the two-photon resonance condition is satisfied. Microwave and optical implementations are discussed with gate fidelities being evaluated against several decoherence mechanisms such as atomic velocity fluctuations or the presence of a weak magnetic field. The use of coherent states for both polarization states is investigated to assess the entanglement capability of the proposed quantum gates.
Two Qubits Entanglement Dynamics in 1D Heisenberg Chain with Intrinsic Decoherence
Institute of Scientific and Technical Information of China (English)
SHAO Bin; ZHANG Li-li; ZOU Jian
2006-01-01
To reveal how the decoherence modifies the time evolution of the entanglement of quantum system,the intrinsic decoherence approach and the entanglement of formation are used, and the time evolution of entanglement for two-qubit 1D quantum Heisenberg model in an external uniform magnetic field is derived. It is shown that the external magnetic field can strengthen the effects of the intrinsic decoherence on the entanglement of the system.
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction.
One-step quantum phase gate in the ultrastrong coupling regime of circuit QED
Xu, Xuexin; Liu, Xin; Liao, Qinghong; Zhou, Keya; Liu, Shutian
2017-09-01
In a previous publication (Phys Rev Lett 108: 120501, 2012), Romero et al. proposed an ultrastrong coupling circuit QED system that can implement a two-qubit quantum phase gate with four controlling pulses. Based on this architecture, we demonstrate that an ultrafast two-qubit phase gate can also be realized with only one oscillation and lower coupling strengths. In our operation scheme, two identical qubits evolve synchronously under a single pulse with a duration determined by a specific coupling strength. The phase gate can also be obtained periodically. The influences of parameter fluctuations are estimated. We demonstrate that the fidelities can be greater than 99% if the parameter fluctuations are controlled within 5%.
Manipulating the sudden death of entanglement in two-qubit atomic systems
Energy Technology Data Exchange (ETDEWEB)
Hussain, Mahmood Irtiza; Tahira, Rabia; Ikram, Manzoor [COMSATS Institute of Information Technology, Islamabad (Pakistan)
2011-10-15
We investigate the entanglement dynamics of a general two-qubit system in a noisy environment presenting analytical descriptions of the time evolution of entanglement having some unitary operations after its evolution in dissipative environments. We show that quantum gates (unitary operators) and bath switching can change the subsequent dynamics of entanglement. For this purpose, we consider {sigma}{sub x} and bath switching operations that change the disentanglement time from finite to infinite.
Coxeter groups $A_{4}$, $B_{4}$ and $D_{4}$ for two-qubit systems
Indian Academy of Sciences (India)
Ramazan Koç; M Yakup Haciibrahimoğlu; Mehmet Koca
2013-08-01
The Coxeter–Weyl groups $W(A_{4})$, $W(B_{4})$ and $W(D_{4})$ have proven very useful for two-qubit systems in quantum information theory. A simple technique is employed to construct the unitary matrix representations of the groups, based on quaternionic transformation of the usual reflection matrices. The von Neumann entropy of each reduced density matrix is calculated. It is shown that these unitary matrix representations are naturally related to various universal quantum gates and they lead to entangled states. Canonical decomposition of generators in terms of fundamental gate representations is given to construct the quantum circuits.
A scheme of quantum phase gate for trapped ion
Institute of Scientific and Technical Information of China (English)
Cai Jian-Wu; Fang Mao-Fa; Zheng Xiao-Juan; Liao Xiang-Ping
2007-01-01
We propose a scheme to implement two-qubit controlled quantum phase gate(CQPG) via a single trapped twolevel ion located in the standing wave field of a quantum cavity, in which the trap works beyond the Lamb-Dicke limit. When the light field is resonant with the atomic transition |g〉←→|e〉of the ion located at the antinode of the standing wave, we can perform CQPG between the internal and external states of the trapped ion; while the frequency of the light field is chosen to be resonant with the first red sideband of the collective vibrational mode of the ion located at the node of the standing wave, we can perform CQPG between the cavity mode and the collective vibrational mode of the trapped ion. Neither the Lamb-Dicke approximation nor the assistant classical laser is needed. Also we can generate a GHZ state if assisted with a classical laser.
Use of non-adiabatic geometric phase for quantum computing by NMR.
Das, Ranabir; Kumar, S K Karthick; Kumar, Anil
2005-12-01
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.
Zhu, Chengjie; Huang, Guoxiang
2011-11-07
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
Hosten, O.; Krishnakumar, R.; Engelsen, N. J.; Kasevich, M. A.
2016-06-01
Quantum metrology exploits entangled states of particles to improve sensing precision beyond the limit achievable with uncorrelated particles. All previous methods required detection noise levels below this standard quantum limit to realize the benefits of the intrinsic sensitivity provided by these states. We experimentally demonstrate a widely applicable method for entanglement-enhanced measurements without low-noise detection. The method involves an intermediate quantum phase magnification step that eases implementation complexity. We used it to perform squeezed-state metrology 8 decibels below the standard quantum limit with a detection system that has a noise floor 10 decibels above the standard quantum limit.
Understanding quantum phase transitions
Carr, Lincoln
2010-01-01
Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivity and display fundamental aspects of quantum theory, such as strong correlations and entanglement. Over the last two decades, our understanding of QPTs has increased tremendously due to a plethora of experimental examples, powerful new numerical meth
One-Way Information Deficit and Geometry for a Class of Two-Qubit States
Institute of Scientific and Technical Information of China (English)
WANG Yao-Kun; MA Teng; LI Bo; WANG Zhi-Xi
2013-01-01
The work deficit,as introduced by Jonathan Oppenheim et al.[Phys.Rev.Lett.89 (2002) 180402]is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality.In this paper,we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID.The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.
Deterministic Joint Remote Preparation of an Arbitrary Two-Qubit State Using the Cluster State
Institute of Scientific and Technical Information of China (English)
WANG Ming-Ming; CHEN Xiu-Bo; YANG Yi-Xian
2013-01-01
Recently,deterministic joint remote state preparation (JRSP) schemes have been proposed to achieve 100％ success probability.In this paper,we propose a new version of deterministic JRSP scheme of an arbitrary two-qubit state by using the six-qubit cluster state as shared quantum resource.Compared with previous schemes,our scheme has high efficiency since less quantum resource is required,some additional unitary operations and measurements are unnecessary.We point out that the existing two types of deterministic JRSP schemes based on GHZ states and EPR pairs are equivalent.
Remote two-qubit state creation and its robustness
Stolze, J.; Zenchuk, A. I.
2016-08-01
We consider the problem of remote two-qubit state creation using the two-qubit excitation pure initial state of the sender. The communication line is based on the optimized boundary-controlled chain with two pairs of properly adjusted coupling constants. We show that the communication line can be characterized by a set of parameters independent of the initial state of the sender. These parameters are permanent attributes of a communication line and can be either calculated theoretically or measured in experiment. In particular, they determine the creatable subregion of the receiver's state space. The creation of a particular state within the creatable region is achieved by a proper choice of the independent parameters of the sender's initial state (control parameters) and reduces to the solvability of a certain system of algebraic equations. The creation of the two-qubit Werner state is considered as an example. We also study the effects of imperfections of the chain on the state creation.
Entangled Bloch spheres: Bloch matrix and two-qubit state space
Gamel, Omar
2016-06-01
We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parametrize and visualize the two-qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch spheres with superimposed correlation axes. It is shown that unitary transformations, local or nonlocal, have simple interpretations as axis rotations or mixing of certain degrees of freedom. The nonlocal unitary invariants of the state are then derived in terms of local unitary invariants. The positive partial transpose criterion for entanglement is generalized, and interpreted as a reflection, or a change of a single sign. The formalism is used to characterize maximally entangled states, and generalize two qubit isotropic and Werner states.
Quantum Enhanced Phase Retrieval
Liberman, Liat; Poem, Eilon; Silberberg, Yaron
2015-01-01
The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by quantum states of light. We generalize the iterative Gerchberg-Saxton algorithm to photon correlation measurements on the output plane, rather than the standard intensity measurements. We report a numerical comparison of classical and quantum phase retrieval of a small one-dimensional object of discrete phases from its far-field diffraction. While the classical algorithm was ambiguous and often converged to wrong solutions, quantum light produced a unique reconstruction with smaller errors and faster convergence. We attribute these improvements to a larger Hilbert space that constrains the algorithm.
Institute of Scientific and Technical Information of China (English)
XU Hai-Feng; HAN Lian-Fang
2013-01-01
We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a fourqubit duster-class state and a Bell-class state as the quantum channels.In the scheme,the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs.With their measurement results,the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement.Moreover,the total success probability and classical communication cost of the present protocol are also worked out.
Singh, Manu Pratap; Rajput, Balwant S.
2017-04-01
New set of maximally entangled states (Singh-Rajput MES), constituting orthonormal eigen bases, has been revisited and its superiority and suitability in pattern-association (Quantum Associative Memory, QuAM) have been demonstrated. Using these MES as memory states in the evolutionary process of pattern storage in a two-qubit system, it has been shown that the first two states of Singh-Rajput MES are useful for storing the pattern |11> and the last two of these MES are useful in storing the pattern |10> Recall operations of quantum associate memory (QuAM) have been conducted through evolutionary process in terms of unitary operators by separately choosing Singh-Rajput MES and Bell's MES as memory states and it has been shown that Singh-Rajput MES as valid memory states for recalling the patterns in a two-qubit system are much more suitable than Bell's MES.
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations.The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations.It includes remote state preparation by using any pure entangled states,nonlocal operation implementation using entangled states,entanglement capacity of two-qubit gates and two-qubit gates construction.
Institute of Scientific and Technical Information of China (English)
SU Wan-Jun; SHEN Li-Tuo; WU Huai-Zhi; LIN Xiu
2013-01-01
Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic laser can be used for realizing non-geometric conditional phase gate,and the cavity mode is virtually excited during the gate operation.Thus,the fidelity of the gate operation is insensitive to cavity decay and the fluctuation of the preset laser intensity.The numerical simulation with a realistic set of experimental parameters shows that the gate fidelity 0.987 can be within reached in the near future.
Nonlocal quantum cloning via quantum dots trapped in distant cavities
Institute of Scientific and Technical Information of China (English)
Yu Tao; Zhu Ai-Dong; Zhang Shou
2012-01-01
A scheme for implementing nonlocal quantum cloning via quantum dots trapped in cavities is proposed.By modulating the parameters of the system,the optimal 1 → 2 universal quantum cloning machine,1 → 2 phase-covariant cloning machine,and 1 → 3 economical phase-covariant cloning machine are constructed.The present scheme,which is attainable with current technology,saves two qubits compared with previous cloning machines.
Entanglement Dynamics of Two-Qubit System in Different Types of Noisy Channels
Institute of Scientific and Technical Information of China (English)
SHAN Chuan-Jia; LIU Ji-Bing; CHENG Wei-Wen; LIU Tang-Kun; HUANG Yan-Xia; LI Hong
2009-01-01
In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.
Entanglement Dynamics of Two Qubits in a Common Bath
Ma, Jian; Wang, Xiaoguang; Nori, Franco
2012-01-01
We derive a set of hierarchical equations for qubits interacting with a Lorentz-broadened cavity mode at zero temperature, without using the rotating-wave, Born, and Markovian approximations. We use this exact method to reexamine the entanglement dynamics of two qubits interacting with a common bath, which was previously solved only under the rotating-wave and single-excitation approximations. With the exact hierarchy equation method used here, we observe significant differences in the resulting physics, compared to the previous results with various approximations. Double excitations due to counter-rotating-wave terms are also found to have remarkable effects on the dynamics of entanglement.
Teleportation of an Arbitrary Two-qubit State *
Institute of Scientific and Technical Information of China (English)
庞霖; 严瑛白; 金国藩; 韦辉; 郭履容
2001-01-01
A scheme to teleport an unknown two-qubit state from Alice (the sender) to Bob (the receiver) using two Einstein-Podolsky-Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.
Quantum Discrete Fourier Transform in an Ion Trap System
Institute of Scientific and Technical Information of China (English)
ZHENG Shi-Biao
2007-01-01
We propose two schemes for the implementation of quantum discrete Fourier transform in the ion trap system. In each scheme we design a tunable two-qubit phase gate as the main ingredient. The experimental implementation of the schemes would be an important step toward complex quantum computation in the ion trap system.
Institute of Scientific and Technical Information of China (English)
S. Salimi; A. Mohammadzadet
2011-01-01
Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU（2） coherent states.
Institute of Scientific and Technical Information of China (English)
WANG Zhang-Yin; WANG Dong; LIU Jun; SHI Shou-Hua
2006-01-01
We present a scheme for probabilistically teleporting an arbitrary unknown two-qubit state through a quantum channel made up of two nonidentical non-maximally entangled states. In this scheme, the probabilistic teleportation is realized by using a proper positive operator-valued measure instead of usual projective measurement.
Energy Technology Data Exchange (ETDEWEB)
Dong, Li; Xiu, Xiao-Ming, E-mail: xiuxiaomingdl@126.com [Dalian University of Technology, School of Physics and Optoelectronic Technology (China); Ren, Yuan-Peng [Bohai University, Higher Professional Technical Institute (China); Gao, Ya-Jun [Bohai University, College of Mathematics and Physics (China); Yi, X. X. [Dalian University of Technology, School of Physics and Optoelectronic Technology (China)
2013-01-15
We propose a protocol transferring an arbitrary unknown two-qubit state using the quantum channel of a four-qubit genuine entangled state. Simplifying the four-qubit joint measurement to the combination of Bell-state measurements, it can be realized more easily with currently available technologies.
The sudden Birth and sudden Death of thermal fidelity in a two-qubit XY model
Qin, Li-Guo; Jiang, Ying; Zhang, Hong-Biao
2011-01-01
We study the energy level crossings of the states and thermal fidelity for a two-qubit XY model in the presence of a transverse and inhomogeneous magnetic field. It is shown clearly the effects of the anisotropic factor of the magnetic field through the contour figures of energy level crossing in two subspaces, the isotropy subspace and anisotropy subspace. We calculate the quantum fidelity between the system and the ground state to which the results show the strong effect of the anisotropic factor again. In addition, making use of the transition of Yangian generators in the tensor product space, we study the evolution of the thermal fidelity after the transition. The potential applications of Yangian algebra, as a switch to turn on or off the fidelity, are proposed.
Bidirectional Mapping between a Biphoton Polarization State and a Single-Photon Two-Qubit State
Institute of Scientific and Technical Information of China (English)
LIN Qing
2010-01-01
@@ How to manipulate(operate or measure)single photons efficiently and simply is the basic problem in optical quantum information processing.We first present an efficient scheme to transform a biphoton polarization state to a corresponding single-photon state encoded by its polarization and spatial modes.This single-photon state carries both the information of the controlled and target photons.It will make the realization of bipartite positive-operator-valued measurements efficiently and simply.Moreover,the inverse transformation from the single-photon state back to the corresponding biphoton polarization state is also proposed.Using both the transformations,the realization of the arbitrary two-qubit unitary operation is simple with an M-Z interferometer.All the schemes are feasible with the current experimental technology.
Entanglement, quantum phase transitions and quantum algorithms
Orus, R
2006-01-01
The work that we present in this thesis tries to be at the crossover of quantum information science, quantum many-body physics, and quantum field theory. We use tools from these three fields to analyze problems that arise in the interdisciplinary intersection. More concretely, in Chapter 1 we consider the irreversibility of renormalization group flows from a quantum information perspective by using majorization theory and conformal field theory. In Chapter 2 we compute the entanglement of a single copy of a bipartite quantum system for a variety of models by using techniques from conformal field theory and Toeplitz matrices. The entanglement entropy of the so-called Lipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with that of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of scaling of quantum correlations in quantum phase transitions to the study of quantum algorithms, focusing on Shor's factorization algorithm and quantum algorithms by adiabatic evolution solving a...
Relaxation of coherent states in a two-qubit NMR quadrupole system
Energy Technology Data Exchange (ETDEWEB)
Sarthour, R.S.; Guimaraes, A.P.; Oliveira, I.S. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Azevedo, E.R. de; Bonk, F.A.; Vidoto, E.L.G.; Bonagamba, T.J. [Universidade de Sao Paulo (IFSC/USP), Sao Carlos, SP (Brazil). Inst. de Fisica; Freitas, J.C.C. [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil). Dept. de Fisica
2003-07-01
Full text: Pulse Nuclear Magnetic Resonance (NMR) is one of the most serious candidates as an experimental technique for implementing quantum algorithms. To the present date, this technique is in fact the only one where full demonstrations of quantum algorithms implementations have been carried out, in spite of various technical difficulties. On NMR quantum computers, gates and subroutines are encoded as radiofrequency pulse sequences, which must act over coherent states. These sequences usually take tens of milliseconds to be implemented, and during this time the system relax towards equilibrium. Therefore, studies of relaxation times are very important to the realization of quantum algorithms via NMR. In this work we studied the longitudinal relaxation of various coherent states on the NMR quantum computing two-qubit quadrupole system, {sup 23}Na in C{sub 10}H{sub 21}NaO{sub 4}S liquid crystal at room temperature. Relaxation of pseudo-pure states |00>, |01>, |10>, |11>, pseudo-Bell states |01> + |10> and |00> + |11> and Hadamard states |00> + |01> and |10> + |11> were investigated. Experimental curves follow a multi exponential model of relaxation which takes into account mixed, dipolar magnetic and quadrupolar electric interactions. (author)
Decoherence of two-qubit systems: a random matrix description
Pineda, C.; Gorin, T.; Seligman, T. H.
2007-04-01
We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one-qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the above relation.
Decoherence of two qubit systems: A random matrix description
Pineda, C; Seligman, T H
2007-01-01
We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above.
Theory of remote entanglement via quantum-limited phase-preserving amplification
Silveri, Matti; Zalys-Geller, Evan; Hatridge, Michael; Leghtas, Zaki; Devoret, Michel H.; Girvin, S. M.
2016-06-01
We show that a quantum-limited phase-preserving amplifier can act as a which-path information eraser when followed by heterodyne detection. This "beam splitter with gain" implements a continuous joint measurement on the signal sources. As an application, we propose heralded concurrent remote entanglement generation between two qubits coupled dispersively to separate cavities. Dissimilar qubit-cavity pairs can be made indistinguishable by simple engineering of the cavity driving fields providing further experimental flexibility and the prospect for scalability. Additionally, we find an analytic solution for the stochastic master equation, a quantum filter, yielding a thorough physical understanding of the nonlinear measurement process leading to an entangled state of the qubits. We determine the concurrence of the entangled states and analyze its dependence on losses and measurement inefficiencies.
Entanglement and entropy engineering of atomic two-qubit states
Clark, S G
2002-01-01
We propose a scheme employing quantum-reservoir engineering to controllably entangle the internal states of two atoms trapped in a high finesse optical cavity. Using laser and cavity fields to drive two separate Raman transitions between metastable atomic ground states, a system is realized corresponding to a pair of two-state atoms coupled collectively to a squeezed reservoir. Phase-sensitive reservoir correlations lead to entanglement between the atoms, and, via local unitary transformations and adjustment of the degree and purity of squeezing, one can prepare entangled mixed states with any allowed combination of linear entropy and entanglement of formation.
Robust Adaptive Quantum Phase Estimation
Roy, Shibdas; Huntington, Elanor H
2014-01-01
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara M.
2016-02-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
Institute of Scientific and Technical Information of China (English)
QIN Meng
2013-01-01
We examine entanglement teleportation,characterized by average fidelity,of two-qubit XY Z spin chain under different nonuniform magnetic field.The entanglement teleportation and the fidelity of entanglement teleportation are investigated separately.We show explicitly that the fidelity of entanglement teleportation can be enhanced by changing the direction of the magnetic field.This means that we can always get optimal fidelity by choosing the directions of magnetic field in the process of quantum teleportation.Moreover,the results show that in some cases the ferromagnetic chain aiso is a quaiified candidate in the process of teleportation protocol.
Quantum processes on phase space
Anastopoulos, C
2003-01-01
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for histories; this object is the decoherence functional of the consistent histories approach. If we take phases as well as probabilities as primitive elements of our theory, we abandon Kolmogorov probability and can describe quantum theory in terms of fundamental commutative observables, without being obstructed by Bell's and related theorems. Generalising the theory of stochastic processes, we develop the description of relative phases and probabilities for paths on the classical phase space. This description provides a theory of quantum processes. We identify a number of basic postulates and study its corresponding properties. We strongly emphasise the notion of conditioning and are able to write ``quantum differential equations'' as analogous to stochastic differential equations...
Quantum Shuttle in Phase Space
DEFF Research Database (Denmark)
Novotny, Tomas; Donarini, Andrea; Jauho, Antti-Pekka
2003-01-01
Abstract: We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a crossover from the tunneling to the shuttling regime, thus...... extending the previously found classical results to the quantum domain. Further, a new dynamical regime is discovered, where the shuttling is driven exclusively by the quantum noise....
Revealing novel quantum phases in quantum antiferromagnets on random lattices
Directory of Open Access Journals (Sweden)
R. Yu
2009-01-01
Full Text Available Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions. The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the sample. When doping the system with non-magnetic impurities, novel inhomogeneous phases emerge from the interplay between geometric randomness and quantum fluctuations. In this paper we review our recent work on quantum phase transitions and novel quantum phases realized in disordered quantum magnets. The system inhomogeneity is found to strongly affect phase transitions by changing their universality class, giving the transition a novel, quantum percolative nature. Such transitions connect conventionally ordered phases to unconventional, quantum disordered ones - quantum Griffiths phases, magnetic Bose glass phases - exhibiting gapless spectra associated with low-energy localized excitations.
Quantum Phase Liquids-Fermionic Superfluid without Phase Coherence
Wu, Ya-Jie; Zhou, Jiang; Kou, Su-Peng
2014-01-01
We investigate the two dimensional generalized attractive Hubbard model in a bipartite lattice, and and a "quantum phase liquid" phase, in which the fermions are paired but don't have phase coherence at zero temperature, in analogy to quantum spin liquid phase. Then, two types of topological quantum phase liquids with a small external magnetic field-Z2 quantum phase liquids and chiral quantum phase liquids-are discussed.
Adiabatic quantum computation and quantum phase transitions
Latorre, J I; Latorre, Jose Ignacio; Orus, Roman
2003-01-01
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.
Clark, Susan M; Fu, Kai-Mei C; Ladd, Thaddeus D; Yamamoto, Yoshihisa
2007-07-27
We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broadband optical pulses to rotate electron spins and provide the clock signal to the system. Nonlocal two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and two-qubit gates with operation times comparable to the inverse Zeeman frequency.
Liang, Lin-mei; Li, Cheng-zu
2005-02-01
This Letter presents nonlocality without inequalities for two-qubit mixed states. This Letter was mainly sparked by Cabello's work [Phys. Rev. A 65 (2003) 032108] and is an extension of our recent work [Phys. Lett. A 318 (2003) 300].
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Einstein-Podolsky-Rosen Steerability Criterion for Two-Qubit Density Matrices
Chen, Jing-Ling; Ye, Xiang-Jun; Wu, Chunfeng; Kwek, L C; Oh, C H
2011-01-01
We propose a criterion ${S}=\\lambda_1+\\lambda_2-(\\lambda_1-\\lambda_2)^2<0$ to detect Einstein-Podolsky-Rosen (EPR) steering for arbitrary two-qubit density matrix $\\rho_{AB}$. Here $\\lambda_1,\\lambda_2$ are respectively the minimal and the second minimal eigenvalues of $\\rho^{T_B}_{AB}$, which is the partial transpose of $\\rho_{AB}$. Numerical results suggest that this criterion is a necessary and sufficient condition for demonstrating steerability of two qubits.
Institute of Scientific and Technical Information of China (English)
ZHANG Yong; LONG Gui-Lu; WU Yu-Chun; GUO Guang-Can
2007-01-01
Natural thermal entanglement between two qubits with ⅩⅩⅩ Heisenberg interaction is studied. For the antiferromagnet, increasing coupling strength or decreasing temperature under critical point increases the entanglement.Based on the thermal entanglement as quantum channel, entanglement and information of an input entangled state are transferred via partial teleportation. We find that the entanglement transferred will be lost during the process, and for the entanglement fidelity the partial teleportation is superior to classical communication as concurrence of entangled channel beyond 1/4. We show that both correlation information in input entangled state and individual information of the teleported particle are linearly dissipated. With more entanglement in quantum channel, more entanglement and correlation information can be transferred.
Energy Technology Data Exchange (ETDEWEB)
Mohamed, A.-B.A., E-mail: abdelbastm@yahoo.com [College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al-Aflaj (Saudi Arabia); Faculty of Science, Assiut University, Assiut (Egypt); Joshi, A., E-mail: mcbamji@gmail.com [Physics Department, Adelphi University Garden City, NY 11530 (United States); Department of Physics and Optical Engineering, RHIT, Terra Haute IN 47803 (United States); Hassan, S.S., E-mail: shoukryhassan@hotmail.com [Department of Mathematics, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)
2016-03-15
Several quantum-mechanical correlations, notably, quantum entanglement, measurement-induced nonlocality and Bell nonlocality are studied for a two qubit-system having no mutual interaction. Analytical expressions for the measures of these quantum-mechanical correlations of different bipartite partitions of the system are obtained, for initially two entangled qubits and the two photons are in their vacuum states. It is found that the qubits-fields interaction leads to the loss and gain of the initial quantum correlations. The lost initial quantum correlations transfer from the qubits to the cavity fields. It is found that the maximal violation of Bell’s inequality is occurring when the quantum correlations of both the logarithmic negativity and measurement-induced nonlocality reach particular values. The maximal violation of Bell’s inequality occurs only for certain bipartite partitions of the system. The frequency detuning leads to quick oscillations of the quantum correlations and inhibits their transfer from the qubits to the cavity modes. It is also found that the dynamical behavior of the quantum correlation clearly depends on the qubit distribution angle.
High-fidelity two-qubit gates via dynamical decoupling of local 1 /f noise at the optimal point
D'Arrigo, A.; Falci, G.; Paladino, E.
2016-08-01
We investigate the possibility of achieving high-fidelity universal two-qubit gates by supplementing optimal tuning of individual qubits with dynamical decoupling (DD) of local 1 /f noise. We consider simultaneous local pulse sequences applied during the gate operation and compare the efficiencies of periodic, Carr-Purcell, and Uhrig DD with hard π pulses along two directions (πz /y pulses). We present analytical perturbative results (Magnus expansion) in the quasistatic noise approximation combined with numerical simulations for realistic 1 /f noise spectra. The gate efficiency is studied as a function of the gate duration, of the number n of pulses, and of the high-frequency roll-off. We find that the gate error is nonmonotonic in n , decreasing as n-α in the asymptotic limit, α ≥2 , depending on the DD sequence. In this limit πz-Urhig is the most efficient scheme for quasistatic 1 /f noise, but it is highly sensitive to the soft UV cutoff. For small number of pulses, πz control yields anti-Zeno behavior, whereas πy pulses minimize the error for a finite n . For the current noise figures in superconducting qubits, two-qubit gate errors ˜10-6 , meeting the requirements for fault-tolerant quantum computation, can be achieved. The Carr-Purcell-Meiboom-Gill sequence is the most efficient procedure, stable for 1 /f noise with UV cutoff up to gigahertz.
Phase-selective quantum eraser
Heuer, A.; Pieplow, G.; Menzel, R.
2015-07-01
A quantum-eraser experiment is reported with photon pairs generated by two synchronously pumped parametric down-converters coupled via induced coherence. The complementarity between which-source information and two-photon interference fringe visibility is demonstrated explicitly. Changing the phase in a Mach-Zehnder interferometer allows a continuous transition from wavelike to particlelike behavior of photons.
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Institute of Scientific and Technical Information of China (English)
Hu Xiao-Mian; Liu Jin-Ming
2009-01-01
Quantum teleportation via the entangled channel composed of a two-qubit Heisenberg XYZ model with Dzyaloshinski-Moriya (DM) interaction in the presence of intrinsic decoherenee has been investigated. We find that the initial state of the channel plays an important role in the teleported state and the average fidelity of teleportation. When the initial channel is in the state [ψ1(0)>=a|00> + b|11>, the average fidelity is equal to 1/3 constantly, which is independent of the DM interaction and the intrinsic decoherence effect. But when the channel is initially in the state [ψ2(0)> = c|01) + d|10>, the average fidelity is always larger than 2/3. Moreover, under a certain condition, the average fidelity can be enhanced by adjusting the DM interaction, and the intrinsic decoherence leads to a suppression of the fluctuation of the average fidelity.
Experimental study of entanglement evolution in the presence of bit-flip and phase-shift noises
Liu, Xia; Cao, Lian-Zhen; Zhao, Jia-Qiang; Yang, Yang; Lu, Huai-Xin
2017-10-01
Because of its important role both in fundamental theory and applications in quantum information, evolution of entanglement in a quantum system under decoherence has attracted wide attention in recent years. In this paper, we experimentally generate a high-fidelity maximum entangled two-qubit state and present an experimental study of the decoherence properties of entangled pair of qubits at collective (non-collective) bit-flip and phase-shift noises. The results shown that entanglement decreasing depends on the type of the noises (collective or non-collective and bit-flip or phase-shift) and the number of qubits which are subject to the noise. When two qubits are depolarized passing through non-collective noisy channel, the decay rate is larger than that depicted for the collective noise. When two qubits passing through depolarized noisy channel, the decay rate is larger than that depicted for one qubit.
Holographic quantum computing.
Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus
2008-07-25
We propose to use a single mesoscopic ensemble of trapped polar molecules for quantum computing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields.
Quantum Phase Extraction in Isospectral Electronic Nanostructures
Energy Technology Data Exchange (ETDEWEB)
Moon, Christopher
2010-04-28
Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures possessing matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these 'quantum drums' [degenerate two-dimensional electron states on the Cu(111) surface confined by individually positioned CO molecules] reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.
Topological phases: Wormholes in quantum matter
Schoutens, K.
2009-01-01
Proliferation of so-called anyonic defects in a topological phase of quantum matter leads to a critical state that can be visualized as a 'quantum foam', with topology-changing fluctuations on all length scales.
Quantum phase transitions in constrained Bose systems
Bonnes, Lars
2011-01-01
This doctoral thesis studies low dimensional quantum systems that can be realized in recent cold atom experiments. From the viewpoint of quantum statistical mechanics, the main emphasis is on the detailed study of the different quantum and thermal phases and their transitions using numerical methods, such as quantum Monte Carlo and the Tensor Network Renormalization Group. The first part of this work deals with a lattice Boson model subject to strong three-body losses. In a quantum-Zeno li...
Entropy of phase measurement quantum phase via quadrature measurement
My, R; My, Robert; Uni, Palacky
1995-01-01
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum state. As an explicit example the multiple measurement of quadrature operator is interpreted as quantum phase detection achieving the ultimate resolution predicted by the Fisher information.
Entangling capabilities of symmetric two-qubit gates
Indian Academy of Sciences (India)
Swarnamala Sirsi; Veena Adiga; Subramanya Hegde
2014-08-01
Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin–Meshkov–Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2s have modelled a wide range of problems in physics. Here, we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis $\\{|j = 1,\\langle; = + 1, 0, -12\\}$. Our technique relies on the decomposition of a Hamiltonian in terms of (3) basis matrices. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of () generators. These matrices are constructed out of angular momentum operators J$_x$, J$_y$, J$_z$. We construct and study the properties of perfect entanglers acting on a symmetric subspace, i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.
Dynamical quantum phase transitions (Review Article)
Zvyagin, A. A.
2016-11-01
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.
Rescuing a Quantum Phase Transition with Quantum Noise
Zhang, Gu; Novais, E.; Baranger, Harold U.
2017-02-01
We show that placing a quantum system in contact with an environment can enhance non-Fermi-liquid correlations, rather than destroy quantum effects, as is typical. The system consists of two quantum dots in series with two leads; the highly resistive leads couple charge flow through the dots to the electromagnetic environment, the source of quantum noise. While the charge transport inhibits a quantum phase transition, the quantum noise reduces charge transport and restores the transition. We find a non-Fermi-liquid intermediate fixed point for all strengths of the noise. For strong noise, it is similar to the intermediate fixed point of the two-impurity Kondo model.
A geometric theory of non-local two-qubit operations
Zhang, J; Whaley, K B; Sastry, S; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
We study non-local two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of non-local gates is a 3-Torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-Torus. Since different points on the 3-Torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of non-local gates. We find that exactly half the non-local ga...
Entanglement capacity of two-qubit unitary operator for rank two mixed states
Institute of Scientific and Technical Information of China (English)
DI; YaoMin
2007-01-01
The entanglement capacity of two-qubit unitary operator acting on rank two mixed states in concurrence is discussed. The condition of perfect entangler is the same as that acting on pure states and the entanglement capacity is the mixing parameter v1. For non-perfect entangler, the upper and lower bound of the entanglement capacity are given.……
Measurement-induced two-qubit entanglement in a bad cavity: Fundamental and practical considerations
DEFF Research Database (Denmark)
Julsgaard, Brian; Mølmer, Klaus
2012-01-01
An entanglement-generating protocol is described for two qubits coupled to a cavity field in the bad-cavity limit. By measuring the amplitude of a field transmitted through the cavity, an entangled spin-singlet state can be established probabilistically. Both fundamental limitations and practical...
Entanglement capacity of two-qubit unitary operator for rank two mixed states
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ The entanglement capacity of two-qubit unitary operator acting on rank two mixed states in concurrence is discussed. The condition of perfect entangler is the same as that acting on pure states and the entanglement capacity is the mixing parameter v1. For non-perfect entangler, the upper and lower bound of the entanglement capacity are given.
Classifying the Quantum Phases of Matter
2015-01-01
2013), arXiv:1305.2176. [10] J. Haah, Lattice quantum codes and exotic topological phases of matter , arXiv:1305.6973. [11[ M. Hastings and S...CLASSIFYING THE QUANTUM PHASES OF MATTER CALIFORNIA INSTITUTE OF TECHNOLOGY JANUARY 2015 FINAL TECHNICAL REPORT...REPORT 3. DATES COVERED (From - To) JAN 2012 – AUG 2014 4. TITLE AND SUBTITLE CLASSIFYING THE QUANTUM PHASES OF MATTER 5a. CONTRACT NUMBER FA8750-12-2
Controlled Remote State Preparation of an Arbitrary Two-Qubit State via a Six-Qubit Cluster State
Sang, Ming-huang; Nie, Li-ping
2017-07-01
In this work, we have demonstrated that a six-qubit cluster state can be used to realize the deterministic controlled remote state preparation of an arbitrary two-qubit state by performing only the special two-qubit projective measurements.
Generation and protection of steady-state quantum correlations due to quantum channels with memory
Guo, You-neng; Fang, Mao-fa; Wang, Guo-you; Zeng, Ke
2016-12-01
We have proposed a scheme of the generation and preservation of two-qubit steady-state quantum correlations through quantum channels where successive uses of the channels are correlated. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels, have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of quantum correlations has been discussed in detail. The results show that steady-state entanglement between two initial qubits whose initial states are prepared in a specific family states without entanglement subject to amplitude damping channel with memory can be generated. The entanglement creation is related to the memory coefficient of channel μ . The stronger the memory coefficient of channel μ is, the more the entanglement creation is, and the earlier the separable state becomes the entangled state. Besides, we compare the dynamics of entanglement with that of quantum discord when a two-qubit system is initially prepared in an entangled state. We show that entanglement dynamics suddenly disappears, while quantum discord dynamics displays only in the asymptotic limit. Furthermore, two-qubit quantum correlations can be preserved at a long time in the limit of μ → 1.
Generation and protection of steady-state quantum correlations due to quantum channels with memory
Guo, You-neng; Fang, Mao-fa; Wang, Guo-you; Zeng, Ke
2016-09-01
We have proposed a scheme of the generation and preservation of two-qubit steady-state quantum correlations through quantum channels where successive uses of the channels are correlated. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels, have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of quantum correlations has been discussed in detail. The results show that steady-state entanglement between two initial qubits whose initial states are prepared in a specific family states without entanglement subject to amplitude damping channel with memory can be generated. The entanglement creation is related to the memory coefficient of channel μ . The stronger the memory coefficient of channel μ is, the more the entanglement creation is, and the earlier the separable state becomes the entangled state. Besides, we compare the dynamics of entanglement with that of quantum discord when a two-qubit system is initially prepared in an entangled state. We show that entanglement dynamics suddenly disappears, while quantum discord dynamics displays only in the asymptotic limit. Furthermore, two-qubit quantum correlations can be preserved at a long time in the limit of μ → 1.
Iemini, Fernando; da Silva Souza, Leonardo; Debarba, Tiago; Cesário, André T.; Maciel, Thiago O.; Vianna, Reinaldo O.
2017-05-01
We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.
Phase Information in Quantum Oracle Computing
Machta, J.
1998-01-01
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmissio...
Relative entropy of entanglement of two-qubit Ux-invariant states
Wang, Zhen; Wang, Zhi-Xi
2015-01-01
It is strictly proved that a two-qubit Ux-invariant state reaches its relative entropy of entanglement (REE) by the separable state having the same matrix structure. We also formulate three quadratic equations for the corresponding closest separable state (CSS) of Ux-invariant states by their symmetric property. Thus, the CSS of Ux-invariant state can be provided. Furthermore, to illustrate our result we consider two concrete examples.
Simple Scheme for Directly Measuring Concurrence of Two-Qubit Pure States in One Step
Institute of Scientific and Technical Information of China (English)
YANG Rong-Can; LIN Xiu; HUANG Zhi-Ping; LI Hong-Cai
2009-01-01
In the present work, a simple scheme for the direct measurement of the concurrence of two-qubit pure states is proposed.The scheme is based on trapped ions and only needs one step when the two identical pure states are given.The vibrational mode in our proposal is only virtually excited, which is important in view of decoherence.Furthermore, the scheme is feasible based on current technologies.
Bipartite entanglement in a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field
Institute of Scientific and Technical Information of China (English)
QIN Meng; TIAN Dong-Ping
2009-01-01
This paper investigates the bipartite entanglement of a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. By the concept of negativity, we find that the inhomogeneity of the magnetic field may induce entanglement and the critical magnetic field is independent of Jz. We also find that the entanglement is symmetric with respect to a zero magnetic field. The anisotropy parameter Jz may enhance the entanglement.
Phase space methods for degenerate quantum gases
Dalton, Bryan J; Barnett, Stephen M
2015-01-01
Recent experimental progress has enabled cold atomic gases to be studied at nano-kelvin temperatures, creating new states of matter where quantum degeneracy occurs - Bose-Einstein condensates and degenerate Fermi gases. Such quantum states are of macroscopic dimensions. This book presents the phase space theory approach for treating the physics of degenerate quantum gases, an approach already widely used in quantum optics. However, degenerate quantum gases involve massive bosonic and fermionic atoms, not massless photons. The book begins with a review of Fock states for systems of identical atoms, where large numbers of atoms occupy the various single particle states or modes. First, separate modes are considered, and here the quantum density operator is represented by a phase space distribution function of phase space variables which replace mode annihilation, creation operators, the dynamical equation for the density operator determines a Fokker-Planck equation for the distribution function, and measurable...
The quantum phase operator a review
Barnett, Stephen M
2013-01-01
Describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle since the early days of modern quantum theory. The quantum phase operator was even more problematic with the invention of the maser and laser in the 1950s and 1960s. This problem was not solved until the Pegg-Barnett formalism was developed in the 1980s. Edited by one of the scientists who created this key solution, The Quantum Phase Operator: A Review charts the development of phase and angle operators from their first appearance to modern theory. Bringing together vital works that have been publ
The flat phase of quantum polymerized membranes
Coquand, O
2016-01-01
We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features : quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free standing graphene physics.
Scaling of the local quantum uncertainty at quantum phase transitions
Energy Technology Data Exchange (ETDEWEB)
Coulamy, I.B.; Warnes, J.H.; Sarandy, M.S., E-mail: msarandy@if.uff.br; Saguia, A.
2016-04-29
We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT. - Highlights: • LQU is suitable for the analysis of block correlations. • LQU exhibits pronounced behavior at quantum phase transitions. • LQU exponentially saturates in the quantum search. • Concavity of LQU indicates criticality in the Ising chain.
Quantum computation with ions in microscopic traps
Šašura, Marek; Steane, Andrew M.
2002-12-01
We discuss a possible experimental realization of fast quantum gates with high fidelity with ions confined in microscopic traps. The original proposal of this physical system for quantum computation comes from Cirac and Zoller (Nature 404, 579 (2000)). In this paper we analyse a sensitivity of the ion-trap quantum gate on various experimental parameters which was omitted in the original proposal. We address imprecision of laser pulses, impact of photon scattering, nonzero temperature effects and influence of laser intensity fluctuations on the total fidelity of the two-qubit phase gate.
Quantum Discord of Non-X State
Institute of Scientific and Technical Information of China (English)
YAO Jing-Ying; DONG Yu-Li; ZHU Shi-Qun
2013-01-01
The level surfaces of quantum discord for a class of two-qubit states are investigated when the Bloch vectors (r) and (s) are perpendicularly oriented.The geometric objects of tetrahedron T and octahedron O are deformed.The level surfaces of constant discord are formed by three interaction “tubes” along three orthogonal directions.They shrink to the center when the Bloch vectors are increased and are expanded and cut off by the state tetrahedron T when the quantum discord is increased.In the phase damping channel,the quantum discord keeps approximately a constant when the time increases.
Quantum Fisher information as signature of superradiant quantum phase transition
Wang, T L; Yang, W; Jin, G R; Lambert, N; Nori, F
2013-01-01
The single-mode Dicke model is well-known to undergo a quantum phase transition from the so-called normal phase to the supperradiant phase (hereinafter called the "superradiant quantum phase transition"). Normally, quantum phase transitions are closely related to the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study quantum Fisher information (QFI) of the field mode and that of the atoms in the ground state of the Dicke Hamiltonian. For finite and large enough number of atoms N, our numerical results show that near the critical atom-field coupling, the QFIs of the atomic and the field subsystems can surpass the classical limits, due to the appearance of nonclassical squeezed states. As the coupling increases far beyond the critical point, the two subsystems are in highly mixed states, which degrade the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present analytical results of the QFIs and their relationships with t...
Conductor-insulator quantum phase transitions
Trivedi, Nandini; Valles, James M
2012-01-01
When many particles come together how do they organise themselves? And what destroys this organisation? Combining experiments and theory, this book describes intriguing quantum phases - metals, superconductors and insulators - and transitions between them.
Institute of Scientific and Technical Information of China (English)
Qin Meng; Tian Dong-Ping
2009-01-01
This paper investigates bipartite entanglement of a two-qubit system with anisotropic couplings under all inhomogeneous magnetic field.This work is mainly to investigate the characteristics of a Heisenberg XYZ chain and obtains some meaningful results.By the concept of negativity,it finds that the inhomogeneity of magnetic field may induce entanglement and the critical magnetic field is independent of Jz.The inhomogeneous magnetic field can increase the value of critical magnetic field Bc.It also finds that the magnetic field not only suppresses the entanglement but also can induce it to revival for some time.
Optimal feedback control of two-qubit entanglement in dissipative environments
Rafiee, Morteza; Nourmandipour, Alireza; Mancini, Stefano
2016-07-01
We study the correction of errors intervening in two qubits dissipating into their own environments. This is done by resorting to local feedback actions with the aim of preserving as much as possible the initial amount of entanglement. Optimal control is found first by gaining insights from the subsystem purity and then by numerical analysis on the concurrence. This is tantamount to a double optimization on the actuation and on the measurement processes. Repeated feedback action is also investigated, thus paving the way for a continuous-time formulation and a solution of the problem.
A study of two-qubit density matrices with fermionic purifications
Energy Technology Data Exchange (ETDEWEB)
Szalay, Szilard; Levay, Peter; Nagy, Szilvia; Pipek, Janos [Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111 Budafoki ut 8 (Hungary)
2008-12-19
We study 12 parameter families of two-qubit density matrices, arising from a special class of two-fermion systems with four single-particle states or alternatively from a four-qubit state with amplitudes arranged in an antisymmetric matrix. We calculate the Wootters concurrences and the negativities in a closed form and study their behavior. We use these results to show that the relevant entanglement measures satisfy the generalized Coffman-Kundu-Wootters formula of distributed entanglement. An explicit formula for the residual tangle is also given. The geometry of such density matrices is elaborated in some detail. In particular, an explicit form for the Bures metric is given.
On Arbitrary Phases in Quantum Amplitude Amplification
Hoyer, P
2000-01-01
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\\tan(\\phi/2)=\\tan(\\phi/2)(1-2a)$, where $\\phi$ and $\\phi$ are the phases used and where $a$ is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $\\frac{1}{\\sqrt{a}}$ can be tolerated in amplitude amplification.
Joint estimation of phase and phase diffusion for quantum metrology
Vidrighin, Mihai D; Genoni, Marco G; Jin, Xian-Min; Kolthammer, W Steven; Kim, M S; Datta, Animesh; Barbieri, Marco; Walmsley, Ian A
2014-01-01
Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase shift and the amplitude of phase diffusion, at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states -- split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental setup for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.
Formulation and picture of quantum phase
Institute of Scientific and Technical Information of China (English)
YAO ZhiXin; ZHONG JianWei; PAN BaiLiang
2009-01-01
Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form e~(iφ)-cosφ+i sinφin the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ= π/2, the correlative quantum phase is a unitary pure imaginary number e~(iπ/2)=cos(π/2)+i sin(π/2) = i. By using a photon state-vector function that is the general solution of photon Schrodinger equation and can completely describe a photon's behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.
Formulation and picture of quantum phase
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on the concept of classical phase,we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator,which corresponds to the angular position θ in an actual physical space with a classical reference frame,but it takes a complex exponential form eiθ≡cosθ +i sinθ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular,when θ = π/2,the correlative quantum phase is a unitary pure imaginary number eiπ/2 ≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schrdinger equation and can completely describe a photon’s behavior,we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.
Quantum Phase Transitions in a Finite System
Leviatan, A
2006-01-01
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of first-order with an arbitrary barrier.
Discord under the influence of a quantum phase transition
Institute of Scientific and Technical Information of China (English)
Wang Lin-cheng; Shen Jian; Yi Xue-Xi
2011-01-01
This paper studies the discord of a bipartite two-level system coupling to an XY spin-chain environment in a transverse field and investigates the relationship between the discord property and the environment's quantum phase transition. The results show that the quantum discord is also able to characterize the quantum phase transitions. We also discuss the difference between discord and entanglement, and show that quantum discord may reveal more general information than quantum entanglement for characterizing the environment's quantum phase transition.
Compressed quantum computation using a remote five-qubit quantum computer
Hebenstreit, M.; Alsina, D.; Latorre, J. I.; Kraus, B.
2017-05-01
The notion of compressed quantum computation is employed to simulate the Ising interaction of a one-dimensional chain consisting of n qubits using the universal IBM cloud quantum computer running on log2(n ) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer with a limited amount of runs. As a solution, we propose to use validating circuits, that is, to run independent controlled quantum circuits of similar complexity to the circuit of interest.
Quantum Phases of Matter in Optical Lattices
2015-06-30
findings contained in this report are those of the author(s) and should not contrued as an official Department of the Army position , policy or...phases in beyond-standard optical lattices”, Oct 25, 2013 Nikhil Monga, John Shumway, Kaden Hazzard, Erich Mueller, Steven Desch, " Renormalization of...Ho, “Cold Atoms in Curved Space ”, Quantum Materials-Perspectives and Opportunities, The Rice Center for Quantum Materials, December 15, 2014
The geometric phase in quantum physics
Energy Technology Data Exchange (ETDEWEB)
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Energy Technology Data Exchange (ETDEWEB)
Vargas-MartInez, J M; Moya-Cessa, H [INAOE, Coordinacion de Optica, Apartado Postal 51 y 216, 72000 Puebla (Mexico)
2004-03-01
Based on the phase operator introduced by Turski we present a formalism for phase that passes Barnett-Pegg's acid test giving the correct phase variance for a number state. We show that this formalism is in fact the radially integrated Q-function formalism that is used to obtain phase properties. It is also shown that depending on the commutation relation used for phase and number, the phase fluctuations for a coherent state obtained from the integrated Q-function tend to the 1/2{rho}{sup 2} limit while for the Pegg-Barnett formalism they tend to 1/(4{rho}{sup 2}+3/{pi}{sup 2}) just like the fluctuations from the integrated Wigner function, where {rho} is the amplitude of the coherent state00.
Energy Technology Data Exchange (ETDEWEB)
Klimov, Andrei B [Departamento de FIsica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, Luis L [Departamento de Optica, Facultad de FIsica, Universidad Complutense, 28040 Madrid (Spain); Guise, Hubert de [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada); Bjoerk, Gunnar [Department of Microelectronics and Information Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista (Sweden)
2004-04-02
We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of dealing with this problem is through phase operators associated with the algebra su(3). The rather unusual properties of these phases are caused by the small dimension of the system and are explored in detail. We also examine the positive operator-valued measures that can describe the qutrit phase properties.
Disentanglement of Two Qubits Coupled to an XY Spin Chain at Finite Temperature
Institute of Scientific and Technical Information of China (English)
NIE Jing; WANG Lin-Cheng; YI Xue-Xi
2009-01-01
The disentanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied in this letter. The dynamical process of the entanglement is numerically and anaiytically investigated. We find that thermal effects can enhance disentanglement if the entangled initial state of the central spins does not in the decoherenee free space. The critical phenomenon of quantum phase transitions reflected in the disentanglement can be washed out by the thermal effect eventually.
Entropic Phase Maps in Discrete Quantum Gravity
Directory of Open Access Journals (Sweden)
Benjamin F. Dribus
2017-06-01
Full Text Available Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 ⊂ C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics.
Critical assessment of two-qubit post-Markovian master equations
Campbell, S; Mazzola, L; Gullo, N Lo; Vacchini, B; Busch, Th; Paternostro, M
2012-01-01
A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.
Entanglement dynamics of a two-qubit system coupled individually to Ohmic baths
Duan, Liwei; Chen, Qinghu; Zhao, Yang
2013-01-01
The Davydov D1 ansatz, which assigns an individual bosonic trajectory to each spin state, is an efficient, yet accurate trial state for time-dependent variation of the the spin-boson model [J. Chem. Phys. 138, 084111 (2013)]. In this work, the Dirac-Frenkel time-dependent variational procedure utilizing the Davydov D1 ansatz is implemented to study entanglement dynamics of two qubits under the influence of two independent baths. The Ohmic spectral density is used without the Born-Markov approximation or the rotating-wave approximation. In the strong coupling regime the entanglement sudden death is always found to exist, while at the intermediate coupling regime, the entanglement dynamics calculated by Davydov D1 ansatz displays oscillatory behavior in addition to entanglement sudden death and revival.
Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain
Institute of Scientific and Technical Information of China (English)
SHAN Chuan-Jia; CHENG Wei-Wen; LIU Tang-Kun; LIU Ji-Bing; WEI Hua
2008-01-01
Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence or decoherence.
Complete multiple round quantum dense coding with quantum logical network
Institute of Scientific and Technical Information of China (English)
LI ChunYan; LI XiHan; DENG FuGuo; ZHOU Ping; ZHOU HongYu
2007-01-01
We present a complete multiple round quantum dense coding scheme for improving the source capacity of that introduced recently by Zhang et al. The receiver resorts to two qubits for storing the four local unitary operations in each round.
Robust quantum data locking from phase modulation
Lupo, Cosmo; Wilde, Mark M.; Lloyd, Seth
2014-08-01
Quantum data locking is a uniquely quantum phenomenon that allows a relatively short key of constant size to (un)lock an arbitrarily long message encoded in a quantum state, in such a way that an eavesdropper who measures the state but does not know the key has essentially no information about the message. The application of quantum data locking in cryptography would allow one to overcome the limitations of the one-time pad encryption, which requires the key to have the same length as the message. However, it is known that the strength of quantum data locking is also its Achilles heel, as the leakage of a few bits of the key or the message may in principle allow the eavesdropper to unlock a disproportionate amount of information. In this paper we show that there exist quantum data locking schemes that can be made robust against information leakage by increasing the length of the key by a proportionate amount. This implies that a constant size key can still lock an arbitrarily long message as long as a fraction of it remains secret to the eavesdropper. Moreover, we greatly simplify the structure of the protocol by proving that phase modulation suffices to generate strong locking schemes, paving the way to optical experimental realizations. Also, we show that successful data locking protocols can be constructed using random code words, which very well could be helpful in discovering random codes for data locking over noisy quantum channels.
Quantum Fourier Transform and Phase Estimation in Qudit System
Institute of Scientific and Technical Information of China (English)
CAO Ye; PENG Shi-Guo; ZHENG Chao; LONG Gui-Lu
2011-01-01
The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc.In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case.They can be seen as subroutines in a main program run in a qudit quantum computer, and the quantum circuits are given.
Olaya-Castro, Alexandra; Johnson, Neil F.; Quiroga, Luis
2004-08-01
We present an efficient scheme for the controlled generation of pure two-qubit states possessing any desired degree of entanglement and a prescribed symmetry. This is achieved in two-qubit-cavity QED systems (e.g., cold-trapped ions and flying atoms) via on-resonance ion- or atom-cavity couplings, which are time dependent and asymmetric, yielding a trapping vacuum state condition which does not arise for identical couplings. A duality in the role of the coupling ratio yields states with a given concurrence but opposing symmetries. Both the trapping state condition and the resulting entanglement power are robust against decoherence channels.
Controllable coherent population transfers in superconducting qubits for quantum computing.
Wei, L F; Johansson, J R; Cen, L X; Ashhab, S; Nori, Franco
2008-03-21
We propose an approach to coherently transfer populations between selected quantum states in one- and two-qubit systems by using controllable Stark-chirped rapid adiabatic passages. These evolution-time insensitive transfers, assisted by easily implementable single-qubit phase-shift operations, could serve as elementary logic gates for quantum computing. Specifically, this proposal could be conveniently demonstrated with existing Josephson phase qubits. Our proposal can find an immediate application in the readout of these qubits. Indeed, the broken parity symmetries of the bound states in these artificial atoms provide an efficient approach to design the required adiabatic pulses.
A Gaussian measure of quantum phase noise
Schleich, Wolfgang P.; Dowling, Jonathan P.
1992-01-01
We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.
Dominance of quantum over classical correlations: entropic and geometric approach
Walczak, Zbigniew; Wintrowicz, Iwona; Zakrzewska, Katarzyna
2013-01-01
Recently, it has been shown that there exist quantum states for which quantum correlations dominate over classical correlations. Inspired by this observation, we investigate the problem of quantum correlations dominance for two-qubit Bell diagonal states in the Ollivier--Zurek paradigm, using both entropic and geometric approach to quantification of classical and quantum correlations. In particular, we estimate numerically the amount of two-qubit Bell diagonal states for which quantum correla...
Exotic quantum phase transitions of strongly interacting topological insulators
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O (4 ) nonlinear sigma model field theory with a Θ term.
Quantum phase transitions with dynamical flavors
Bea, Yago; Ramallo, Alfonso V
2016-01-01
We study the properties of a D6-brane probe in the ABJM background with smeared massless dynamical quarks in the Veneziano limit. Working at zero temperature and non-vanishing charge density, we show that the system undergoes a quantum phase transition in which the topology of the brane embedding changes from a black hole to a Minkowski embedding. In the unflavored background the phase transition is of second order and takes place when the charge density vanishes. We determine the corresponding critical exponents and show that the scaling behavior near the quantum critical point has multiplicative logarithmic corrections. In the background with dynamical quarks the phase transition is of first order and occurs at non-zero charge density. In this case we compute the discontinuity of several physical quantities as functions of the number $N_f$ of unquenched quarks of the background.
Quantum phase transitions with dynamical flavors
Bea, Yago; Jokela, Niko; Ramallo, Alfonso V.
2016-07-01
We study the properties of a D6-brane probe in the Aharony-Bergman-Jafferis-Maldacena (ABJM) background with smeared massless dynamical quarks in the Veneziano limit. Working at zero temperature and nonvanishing charge density, we show that the system undergoes a quantum phase transition in which the topology of the brane embedding changes from a black hole to a Minkowski embedding. In the unflavored background the phase transition is of second order and takes place when the charge density vanishes. We determine the corresponding critical exponents and show that the scaling behavior near the quantum critical point has multiplicative logarithmic corrections. In the background with dynamical quarks the phase transition is of first order and occurs at nonzero charge density. In this case we compute the discontinuity of several physical quantities as functions of the number Nf of unquenched quarks of the background.
Characterizing the dynamics of quantum discord under phase damping with POVM measurements
Institute of Scientific and Technical Information of China (English)
蒋峰建; 叶剑锋; 闫新虎; 吕海江
2015-01-01
In the analysis of quantum discord, the minimization of average entropy traditionally involved over orthogonal projec-tive measurements may be attained at more optimal decompositions by using the positive-operator-valued measure (POVM) measurements. Taking advantage of the quantum steering ellipsoid in combination with three-element POVM optimization, we show that, for a family of two-qubit X states locally interacting with Markovian non-dissipative environments, the decay rates of quantum discord show smooth dynamical evolutions without any sudden change. This is in contrast to two-element orthogonal projective measurements, in which case the sudden change of the decay rates of quantum and classical decoher-ences may be a common phenomenon. Notwithstanding this, we find that a subset of X states (including the Bell diagonal states) involving POVM optimization can still preserve the sudden change character as usual.
General Phase Matching Condition for Quantum Searching
Long, G L; Sun, Y; Long, Gui-Lu; Xiao, Li; Sun, Yang
2001-01-01
We present a general phase matching condition for the quantum search algorithm with arbitrary unitary transformation and arbitrary phase rotations. We show by an explicit expression that the phase matching condition depends both on the unitary transformation U and the initial state. Assuming that the initial amplitude distribution is an arbitrary superposition sin\\theta_0 |1> + cos\\theta_0 e^{i\\delta} |2> with |1> = {1 / sin\\beta} \\sum_k |\\tau_k> and |2> = {1 / cos\\beta} \\sum_{i \
Institute of Scientific and Technical Information of China (English)
QIAN Li; FANG Jian-Xing
2009-01-01
We study the effects of Dzyaloshinski-Moriya(DM)interaction on entanglement and teleportation in a two-qubit Ising system with intrinsic decoherence taken into account.It is found that for the unentangled state,DM interaction is a benefit for entanglement and teleportation.
Emergence of Decoherence as Phenomenon in Quantum Phase Transition
Quan, H T; Liu, X F; Sun, C P
2005-01-01
We consider the intrinsic relation between the appearance of classicality of a quantum system and the occurrence of quantum phase transition (QPT) in the environment surrounding this system, and study in detail the novel mechanism of quantum decoherence based on QPT with a generalized Hepp-Coleman model where the quantum system is a two level system and the environment is the Ising spin chain interacting with the quantum system. It is discovered that, the quantum decoherence of the quantum system can be accompanied by the quantum critical phenomenon induced by the effective transverse back-action of the quantum system on the environment.
Phase Diagram in Quantum Chromodynamics
Apostol, M
2013-01-01
It is suggested that the hadronization of the quark-gluon plasma is a first-order phase transition described by a critical curve in the temperature-(quark) density plane which terminates in a critical point. Such a critical curve is derived from the van der Waals equation and its parameters are estimated by using the theoretical approach given in M. Apostol, Roum. Reps. Phys. 59 249 (2007); Mod. Phys. Lett. B21 893 (2007). The main assumption is that quark-gluon plasma created by high-energy nucleus-nucleus collisions is a gas of ultrarelativistic quarks in equilibrium with gluons (vanishing chemical potential, indefinite number of quarks). This plasma expands, gets cool and dilute and hadronizes at a certain transition temperature and transition density. The transition density is very close to the saturation density of the nuclear matter and, it is suggested that both these points are very close to the critical point n~1fm^{-3} (quark density) and T~200MeV (temperature).
Quantum phase transition and entanglement in Li atom system
Institute of Scientific and Technical Information of China (English)
2008-01-01
By use of the exact diagonalization method, the quantum phase transition and en- tanglement in a 6-Li atom system are studied. It is found that entanglement appears before the quantum phase transition and disappears after it in this exactly solvable quantum system. The present results show that the von Neumann entropy, as a measure of entanglement, may reveal the quantum phase transition in this model.
Phase diagram of quantum square ice
Henry, Louis-Paul; Holdsworth, Peter; Mila, Frederic; Roscilde, Tommaso
2013-03-01
We have investigated the ground-state and finite-temperature phase diagram of quantum square ice - realized by the transverse-field Ising model on a checkerboard lattice - using both linear spin-wave (LSW) theory and quantum Monte Carlo (QMC). We generalize the model with different couplings between nearest (J1) and next-to-nearest (J2) neighbors on the checkerboard lattice. Our QMC approach generalizes the loop algorithm - very efficient in the study of constrained classical systems - to a ``brane algorithm'' for quantum systems. At the LSW level the vast degeneracy of the ground-state for J1 =J2 and J2 >J1 remains intact; moreover LSW theory breaks down in extended regions of the phase diagram, pointing at non-classical states. Our QMC study goes beyond perturbative schemes and addresses directly the nature of the low-temperature phases. We have critically examined the possibility of a resonating-plaquette state for J1 =J2 , suggested by degenerate perturbation theory on the ice-rule manifold for weak fields. Our QMC results for finite fields confirm the absence of Néel or collinear order, but they do not confirm the presence of resonating-plaquette order, pointing at a possibly more complex non-classical state.
Most robust and fragile two-qubit entangled states under depolarizing channels
Pang, Chao-Qian; Jiang, Yue; Liang, Mai-Lin
2012-01-01
In the two-qubit system under the local depolarizing channels, the most robust and the most fragile states for a given concurrence or negativity are derived. For the one-sided channel, with the aid of the evolution equation for entanglement given by Konrad \\emph{et al.} [Nat. Phys. 4, 99 (2008)], the pure states are proved to be the most robust. Based on a generalization of the evolution equation, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are proved to be the most robust for a fixed concurrence, but is the most fragile with a given negativity when the channel is uniform. Under the uniform channel, for a given negativity, the most robust states are the ones with the maximal concurrence, which are also the most fragile states when the concurrence is given in the region of [1/2,1]. When the entanglement approaches zero, the most fragile states for a given negativity become the pure st...
Phase Transition in Loop Quantum Gravity
Mäkelä, Jarmo
2016-01-01
We point out that with a specific counting of states loop quantum gravity implies that black holes perform a phase transition at a certain characteristic temperature $T_C$. In this phase transition the punctures of the spin network on the stretched horizon of the black hole jump, in effect, from the vacuum to the excited states. The characteristic temperature $T_C$ may be regarded as the lowest possible temperature of the hole. From the point of view of a distant observer at rest with respect to the hole the characteristic temperature $T_C$ corresponds to the Hawking temperature of the hole.
On Quantum Mechanics on Noncommutative Quantum Phase Space
Institute of Scientific and Technical Information of China (English)
A.E.F. DjemaI; H. Smail
2004-01-01
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.
Three qubit quantum phase gate based on cavity QED
Chang, Juntao; Zubairy, M. Suhail
2004-10-01
We describe a three qubit quantum phase gate in which the three qubits are represented by the photons in a three-modes optical cavity. This gate is implemented by passing a four-level atom in a cascade configuration through the cavity. We shall discuss the application of such a quantum phase gate to quantum searching.
Ultrafast quantum computation in ultrastrongly coupled circuit QED systems.
Wang, Yimin; Guo, Chu; Zhang, Guo-Qiang; Wang, Gangcheng; Wu, Chunfeng
2017-03-10
The latest technological progress of achieving the ultrastrong-coupling regime in circuit quantum electrodynamics (QED) systems has greatly promoted the developments of quantum physics, where novel quantum optics phenomena and potential computational benefits have been predicted. Here, we propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a transmission line resonator (TLR), and two more TLRs are coupled to the ultrastrongly-coupled system for assistant. The nontrivial unconventional geometric phase gate between the two flux qubits is achieved based on close-loop displacements of the three-mode intracavity fields. Moreover, as there are three resonators contributing to the phase accumulation, the requirement of the coupling strength to realize the two-qubit gate can be reduced. Further reduction in the coupling strength to achieve a specific controlled-phase gate can be realized by adding more auxiliary resonators to the ultrastrongly-coupled system through superconducting quantum interference devices. We also present a study of our scheme with realistic parameters considering imperfect controls and noisy environment. Our scheme possesses the merits of ultrafastness and noise-tolerance due to the advantages of geometric phases.
Quantum Phase Imaging using Spatial Entanglement
Lu, Chien-Hung; Sun, Xiaohang; Fleischer, Jason W
2015-01-01
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD cam...
Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip.
Paesani, S; Gentile, A A; Santagati, R; Wang, J; Wiebe, N; Tew, D P; O'Brien, J L; Thompson, M G
2017-03-10
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, nonfault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a silicon quantum photonic device. The approach is verified to be well suited for prethreshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed.
Hu, Yao-Hua; Tao, Ya-Ping; Tan, Yong-Gang; Yang, Hai-Feng
2017-02-01
Considering X-states the density matrixes of which look like the letter X, we propose a weak measurement-based entanglement protection protocol of two-qubit X-states under local amplitude damping channels using weak measurement and reversal operation. It is shown that, with increase of the decoherence parameter, the entanglement attenuates rapidly owing to the amplitude damping noise and even experiences entanglement sudden death (ESD). However, the entanglement under the weak measurement and reversal operation is always much stronger than the entanglement undergoing the amplitude damping decoherence. These results reflect that entanglement of two-qubit X-states from amplitude damping decoherence can be protected, and ESD can be circumvented by increasing the weak measurement strength.
Generation of concurrence between two qubits locally coupled to a one-dimensional spin chain
Nag, Tanay; Dutta, Amit
2016-08-01
We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance d . Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of d when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the nonequilibrium situations while the latter is created by a sudden but global change of the environmental transverse field is that the two qubits become maximally entangled for the critical quenching. Following a nonequilibrium evolution of the spin chain, our study for d ≠0 indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by d as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution; the concurrence can be enhanced by a higher number of independent channels. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the nonequilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined nontrivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate. We further establish that the maximally and minimally decohering
Optically induced phase transition of excitons in coupled quantum dots
Institute of Scientific and Technical Information of China (English)
Chen Zi-Dong
2008-01-01
The weak classical light excitations in many semiconductor quantum dots have been chosen as important solidstate quantum systems for processing quantum information and implementing quantum computing. For strong classical light we predict theoretically a novel phase transition as a function of magnitude of this classical light from the deformed to the normal phases in resonance case, and the essential features of criticality such as the scaling behaviour, critical exponent and universality are also present in this paper.
Quantum Dynamics of Magnetic and Electric Dipoles and Berry's Phase
Furtado, C; Furtado, Claudio
2003-01-01
We study the quantum dynamics of neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the Berry's quantum phase. A series of field configurations where this phase would be found are presented. A generalized Casella-type effect is found in one these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.
Dynamical phase transitions in quantum mechanics
Directory of Open Access Journals (Sweden)
Rotter Ingrid
2012-02-01
Full Text Available The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points, the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model and those of highly excited nuclear states (described by random ensembles differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
Quantum correlation and quantum phase transition in the one-dimensional extended Ising model
Zhang, Xi-Zheng; Guo, Jin-Liang
2017-09-01
Quantum phase transitions can be understood in terms of Landau's symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.
Topology-driven magnetic quantum phase transition in topological insulators.
Zhang, Jinsong; Chang, Cui-Zu; Tang, Peizhe; Zhang, Zuocheng; Feng, Xiao; Li, Kang; Wang, Li-Li; Chen, Xi; Liu, Chaoxing; Duan, Wenhui; He, Ke; Xue, Qi-Kun; Ma, Xucun; Wang, Yayu
2013-03-29
The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.
Photon Cascade from a Single Crystal Phase Nanowire Quantum Dot
DEFF Research Database (Denmark)
Bouwes Bavinck, Maaike; Jöns, Klaus D; Zieliński, Michal
2016-01-01
unprecedented potential to be controlled with atomic layer accuracy without random alloying. We show for the first time that crystal phase quantum dots are a source of pure single-photons and cascaded photon-pairs from type II transitions with excellent optical properties in terms of intensity and line width...... quantum optical properties for single photon application and quantum optics.......We report the first comprehensive experimental and theoretical study of the optical properties of single crystal phase quantum dots in InP nanowires. Crystal phase quantum dots are defined by a transition in the crystallographic lattice between zinc blende and wurtzite segments and therefore offer...
Quantum Phase from the Twin Paradox
Ord, G. N.
2012-05-01
The modern concept of spacetime usually emerges from the consideration of moving clocks on the assumption that world-lines are continuous. In this paper we start with the assumption that natural clocks are digital and that events are discrete. By taking different continuum limits we show that the phase of non-relativistic quantum mechanics and the odd metric of spacetime both emerge from the consideration of discrete clocks in relative motion. From this perspective, the continuum limit that manifests itself in 'spacetime' is an infinite mass limit. The continuum limit that gives rise to the Schrödinger equation retains a finite mass as a beat frequency superimposed on the 'Zitterbewegung' at the Compton frequency. We illustrate this in a simple model in which a Poisson process drives a relativistic clock that gives rise to a Feynman path integral, where the phase is a manifestation of the twin paradox. The example shows that the non-Euclidean character of spacetime and the wave-particle duality of quantum mechanics share a common origin. They both emerge from the necessity that clocks age at rates that are path dependent.
Phase-selective reversible quantum decoherence in cavity QED experiment
Filip, R
2001-01-01
New feasible cavity QED experiment is proposed to analyse reversible quantum decoherence in consequence of quantum complementarity and entanglement. Utilizing the phase selective manipulations with enviroment, it is demonstrated how the complementarity particularly induces a preservation of visibility, whereas quantum decoherence is more progressive due to pronounced entanglement between system and enviroment. This effect can be directly observed using the proposed cavity QED measurements.
PT phase transition in multidimensional quantum systems
Bender, Carl M
2012-01-01
Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken PT symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the PT phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled PT-symmetric Hamiltonians, $H=p^2/2+x^2/2+q^2/2+y^2/2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2/2+r^2/2+z^2/2+igxyz$, and $H=p^2/2+x^2/2+q^2/2+y^2+r^2/2+3z^2/2+igxyz$ are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at $g\\approx 0.1$, $g\\approx 0.04$, $g\\approx 0.1$, and $g\\approx 0.05$. These results suggest that the PT phase transition is a robust phen...
Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate
Energy Technology Data Exchange (ETDEWEB)
Poyatos, J.; Cirac, J. [Departamento de Fisica Aplicada, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain); Zoller, P. [Institut fuer Theoretisch Physik, Universitaet Innsbruck, A-6020, Innsbruck (Austria)
1997-01-01
We show how to fully characterize a quantum process in an open quantum system. We particularize the procedure to the case of a universal two-qubit gate in a quantum computer. We illustrate the method with a numerical simulation of a quantum gate in the ion trap quantum computer. {copyright} {ital 1997} {ital The American Physical Society}
Complete Characterization of a Quantum Process the Two-Bit Quantum Gate
Poyatos, J F; Zoller, P
1997-01-01
We show how to fully characterize a quantum process in an open quantum system. We particularize the procedure to the case of a universal two-qubit gate in a quantum computer. We illustrate the method with a numerical simulation of a quantum gate in the ion trap quantum computer.
Jakobczyk, L
2004-01-01
It is shown that even if the linear entropy of mixed two-qubit state is not smaller then 0.457, Bell - CHSH inequalities can be violated. This contradicts the result obtained in the paper of E. Santos [1].
Linear optics and quantum maps
Aiello, A; Woerdman, J P
2006-01-01
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.
Quantum scaling in many-body systems an approach to quantum phase transitions
Continentino, Mucio
2017-01-01
Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.
A conditional quantum phase gate between two 3-state atoms
Yi, X X; You, L
2002-01-01
We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data-bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data-bus. In addition, it only requires common addressing of the two atoms by external laser fields.
Conditional quantum phase gate between two 3-state atoms.
Yi, X X; Su, X H; You, L
2003-03-07
We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data bus. In addition, it requires only common addressing of the two atoms by external laser fields.
Guo-Hui, Yang; Le, Song
2016-02-01
By taking into account the Dzyaloshinsky-Moriya (DM) interaction under uniform magnetic field, quantum correlation behaviors measured by the measurement-induced nonlocality (MIN) and the geometric measure of discord (GMOD) in a two-qubit XY model are investigated in detail. Turning the different parameters can lead the two kinds of measurements to present different properties. For example, increasing the parameter B(uniform magnetic field), the existing region of MIN is larger than GMOD; MIN can appear the phenomenon of monotonous reduction when the parameter D(Dzyaloshinsky-Moriya interaction) is smaller than one threshold value, while GMOD cannot; MIN monotonously reduces with enhancive value of T(temperature), while GMOD initial experiences a slightly increasing and then decreases. One interesting point is that the more obvious and complicated difference between them are shown from the initial values. This property is both true for the zero temperature and the finite temperature. Through analyzing the limit case of the temperature approaching zero, the analytic solutions give the detailed reasons why have different effect on the initial values. Moreover, from the analytic solutions, we know the initial value of MIN is always larger than or equal to GMOD.
Energy Technology Data Exchange (ETDEWEB)
Rossi, Matteo A. C., E-mail: matteo.rossi@unimi.it [Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano, 20133 Milano (Italy); Paris, Matteo G. A., E-mail: matteo.paris@fisica.unimi.it [Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano, 20133 Milano (Italy); CNISM, Unità Milano Statale, I-20133 Milano (Italy)
2016-01-14
We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where the two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.
Effect of Multiphoton Processes on Geometric Quantum Computation in Superconducting Circuit QED
Institute of Scientific and Technical Information of China (English)
CHEN Chang-Yong
2012-01-01
We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.
Nuclear Binding Near a Quantum Phase Transition
Elhatisari, Serdar; Li, Ning; Rokash, Alexander; Alarcón, Jose Manuel; Du, Dechuan; Klein, Nico; Lu, Bing-nan; Meißner, Ulf-G.; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A.; Lee, Dean; Rupak, Gautam
2016-09-01
How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.
Nuclear binding near a quantum phase transition
Elhatisari, Serdar; Rokash, Alexander; Alarcón, Jose Manuel; Du, Dechuan; Klein, Nico; Lu, Bing-nan; Meißner, Ulf-G; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A; Lee, Dean; Rupak, Gautam
2016-01-01
How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. The existence of the nearby first-order ...
Cyclotomy and Ramanujan sums in quantum phase locking
Planat, M
2003-01-01
Phase locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to define phase-locked quantum states and the corresponding Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are revealed and related to Ramanujan sums in the theory of prime numbers. The phase-number commutator vanishes as in the classical case, but a new type of quantum phase noise emerges in expectation values of phase and phase variance. The employed mathematical procedures also emphasize the isomorphism between algebraic number theory and the theory of quantum entanglement
Phase transitions in open quantum systems
Jung, C; Rotter, I
1999-01-01
We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.
Quantum Key Distribution Network Based on Differential Phase Shift
Institute of Scientific and Technical Information of China (English)
WANG Wan-Ying; WANG Chuan; WEN Kai; LONG Gui-Lu
2007-01-01
Using a series of quantum correlated photon pairs, we propose a theoretical scheme for any-to-any multi-user quantum key distribution network based on differential phase shift. The differential phase shift and the different detection time slots ensure the security of our scheme against eavesdropping. We discuss the security under the intercept-resend attack and the source replacement attack.
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
Universal Quantum Gates Based on Both Geometric and Dynamic Phases in Quantum Dots
Institute of Scientific and Technical Information of China (English)
杨开宇; 朱诗亮; 汪子丹
2003-01-01
A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may be achieved by a mixed approach, composed of dynamic evolution and nonadiabatic geometric phase.
Quantum phase transition of light as a control of the entanglement between interacting quantum dots
Barragan, Angela; Vera-Ciro, Carlos; Mondragon-Shem, Ian
We study coupled quantum dots arranged in a photonic crystal, interacting with light which undergoes a quantum phase transition. At the mean-field level for the infinite lattice, we compute the concurrence of the quantum dots as a measure of their entanglement. We find that this quantity smoothly
Quantum repeater based on cavity QED evolutions and coherent light
Gonţa, Denis; van Loock, Peter
2016-05-01
In the framework of cavity QED, we propose a quantum repeater scheme that uses coherent light and chains of atoms coupled to optical cavities. In contrast to conventional repeater schemes, in our scheme there is no need for an explicit use of two-qubit quantum logical gates by exploiting solely the cavity QED evolution. In our previous work (Gonta and van Loock in Phys Rev A 88:052308, 2013), we already proposed a quantum repeater in which the entanglement between two neighboring repeater nodes was distributed using controlled displacements of input coherent light, while the produced low-fidelity entangled pairs were purified using ancillary (four-partite) entangled states. In the present work, the entanglement distribution is realized using a sequence of controlled phase shifts and displacements of input coherent light. Compared to previous coherent-state-based distribution schemes for two-qubit entanglement, our scheme here relies only upon a simple discrimination of two coherent states with opposite signs, which can be performed in a quantum mechanically optimal fashion via a beam splitter and two on-off detectors. For the entanglement purification, we employ a method that avoids the use of extra entangled ancilla states. Our repeater scheme exhibits reasonable fidelities and repeater rates providing an attractive platform for long-distance quantum communication.
Quantum dynamics of a two-atom-qubit system
Energy Technology Data Exchange (ETDEWEB)
Nguyen Van Hieu; Nguyen Bich Ha [Max-Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D-01187 Dresden (Germany); Le Thi Ha Linh [Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi (Viet Nam)], E-mail: nvhieu@iop.vast.ac.vn
2009-09-01
A physical model of the quantum information exchange between two qubits is studied theoretically. The qubits are two identical two-level atoms, the physical mechanism of the quantum information exchange is the mutual dependence of the reduced density matrices of two qubits generated by their couplings with a multimode radiation field. The Lehmberg-Agarwal master equation is exactly solved. The explicit form of the mutual dependence of two reduced density matrices is established. The application to study the entanglement of two qubits is discussed.
Rydberg-interaction-based quantum gates free from blockade error
Shi, Xiao-Feng
2016-01-01
Accurate quantum gates are basic elements for building quantum computers. There has been great interest in designing quantum gates by using blockade effect of Rydberg atoms recently. The fidelity and operation speed of these gates, however, are fundamentally limited by the blockade error. Here we propose another type of quantum gates, which are based on Rydberg blockade effect, yet free from any blockade error. In contrast to the `blocking' method in previous schemes, we use Rydberg energy shift to realise a rational generalised Rabi frequency so that a novel $\\pi$ phase for one input state of the gate emerges. This leads to an accurate Rydberg-blockade based two-qubit quantum gate that can operate in a $0.1\\mu s$ timescale or faster thanks to that it operates by a Rabi frequency which is comparable to the blockade shift.
Institute of Scientific and Technical Information of China (English)
Yang Bai-Yuan; Fang Mao-Fa; Huang Jiang
2013-01-01
In this paper,the dynamical behavior of entanglement of an uncoupled two-qubit system,which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states,is investigated.The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence.The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different.Furthermore,some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.
Decoherence of Two-qubits Coupled with Reservoirs Studied with New Ket-Bra Entangled State Method
Ren, Yi-Chong; Fan, Hong-Yi
2016-04-01
For the first time we define a so-called Ket-Bra Entangled State (KBES) for two-qubits coupled with reservoirs by introduce an extra fictitious mode vector, and convert the corresponding master equation into Schrödinger-like equation by virtue of this state. Via this approach we concisely obtain the dynamic evolution of two uncoupled qubits each immersed in local thermal noise. Based on this, the decoherence evolution for the extended Werner-like states is derived and how purity and temperature influence the concurrence is analyzed. This KBES method may also be applied to tackling master equations of limited atomic level systems.
Pairwise Quantum Correlations for Superpositions of Dicke States
Xi, Zhengjun; Li, Yongming; Wang, Xiaoguang
2011-01-01
Using the concept of quantum discord (QD), we study the quantum correlation for a class of two-qubit X states with exchange and parity symmetries, whose density matrices have complex off-diagonal elements. We derive an upper bound of the QD, which is independent of the arguments of the complex off-diagonal elements of the reduced two-qubit density matricies. Moreover, for the two-qubit X states obtained from Dicke states and their superposition states, we obtain a compact expression of the QD by numerical check. Finally, we apply the expression to discuss the quantum correlation of the reduced two-qubit states of Dicke states and their superpositions, and the results are compared with those obtained by entanglement of formation (EoF), which is a quantum entanglement measure.
Energy Technology Data Exchange (ETDEWEB)
Hui, Ning-Ju [Department of Applied Physics, Xi' an University of Technology, Xi' an 710054 (China); Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China); Hu, Zheng-Da, E-mail: huyuanda1112@jiangnan.edu.cn [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China)
2017-04-01
We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.
Hui, Ning-Ju; Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin; Hu, Zheng-Da
2017-04-01
We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.
Three-observer Bell inequality violation on a two-qubit entangled state
Schiavon, Matteo; Calderaro, Luca; Pittaluga, Mirko; Vallone, Giuseppe; Villoresi, Paolo
2016-01-01
Bipartite Bell inequalities can be simultaneously violated by two different pairs of observers when weak measurements and signaling is employed. Here we experimentally demonstrate the violation of two simultaneous CHSH inequalities by exploiting a two-photon polarization maximally entangled state. Our results demonstrate that large double violation is experimentally achievable. Our demonstration may have impact for Quantum Key Distribution or certification of Quantum Random Number generators ...
Three-observer Bell inequality violation on a two-qubit entangled state
Schiavon, Matteo; Calderaro, Luca; Pittaluga, Mirko; Vallone, Giuseppe; Villoresi, Paolo
2017-03-01
Bipartite Bell inequalities can simultaneously be violated by two different pairs of observers when weak measurements and signalling is employed. Here, we experimentally demonstrate the violation of two simultaneous CHSH inequalities by exploiting a two-photon polarisation maximally entangled state. Our results demonstrate that large double violation is experimentally achievable. Our demonstration may have impact for Quantum Key Distribution or certification of Quantum Random Number generators based on weak measurements.
Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing
Wheatley, T A; Yonezawa, H; Nakane, D; Arao, H; Pope, D T; Ralph, T C; Wiseman, H M; Furusawa, A; Huntington, E H
2009-01-01
Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both adaptive and non-adaptive quantum smoothing, and show that both are better than their well-known time-asymmetric counterparts (quantum filtering). For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to $2\\sqrt{2}$ times smaller than that from non-adaptive quantum filtering (the standard quantum limit). The experimentally measured improvement is $2.24 \\pm 0.14$.
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
Preon model and cosmological quantum-hyperchromodynamic phase transition
Nishimura, H.; Hayashi, Y.
1987-05-01
From the cosmological viewpoint, we investigate whether or not recent preon models are compatible with the picture of the first-order phase transition from the preon phase to the composite quark-lepton phase. It is shown that the current models accepting the 't Hooft anomaly-matching condition together with quantum hyperchromodynamics are consistent with the cosmological first-order phase transition.
Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
Lukierski, Jerzy
2015-01-01
We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \\mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H. The standard (4+4) -dimensional kappa - deformed covariant quantum phase space spanned by kappa - deformed Minkowski coordinates and commuting momenta generators ({x}_{\\mu },{p}_{\\mu }) is obtained as the subalgebra of \\mathcal{H}. We study further the property that Heisenberg double defines particular quantum spaces with Hopf algebroid structure. We calculate by using purely algebraic methods the explicite Hopf algebroid structure of standard kappa - deformed quantum covariant phase space in Majid-Ruegg bicrossproduct basis. The coproducts for Hopf algebroids are not unique, determined modulo the coproduct gauge freedom. Finally we consider the interpretation of the algebraic description of quantum phase spaces as Hopf bialgebroids.
Energy Technology Data Exchange (ETDEWEB)
Ye, Jinwu, E-mail: jy306@ccs.msstate.edu [Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Department of Physics, Capital Normal University, Beijing 100048 (China); Department of Physics and Astronomy, Mississippi State University, P.O. Box 5167, MS 39762 (United States); Chen, Yan, E-mail: yanchen99@gmail.com [Department of Physics, Surface Physics Laboratory (National Key Laboratory) and Lab of Advanced Materials, Fudan University, Shanghai (China)
2013-04-11
By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from 1/3 (2/3) filling on frustrated lattices such as triangular and Kagome lattice. In a triangular lattice at 1/3, we find a X-CDW, a stripe CDW phase which was found previously by a density operator formalism (DOF). Most importantly, we also find a new CDW-VB phase which has both local CDW and local VB orders, in sharp contrast to a bubble CDW phase found previously by the DOF. In the Kagome lattice at 1/3, we find a VBS phase and a 6-fold CDW phase. Most importantly, we also identify a CDW-VB phase which has both local CDW and local VB orders which was found in previous QMC simulations. We also study several other phases which are not found by the DVM. By analyzing carefully the saddle point structures of the dual gauge fields in the translational symmetry breaking sides and pushing the effective actions slightly away from the commensurate filling f=1/3(2/3), we classified all the possible types of supersolids and analyze their stability conditions. In a triangular lattice, there are X-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. In a Kagome lattice, there are 6-fold CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid (VB-SS). There are also a new kind of supersolid: CDW-VB supersolid. We show that independent of the types of the SS, the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents z=2, ν=1/2, η=0 (with
Experimental demonstration of a programmable quantum computer by NMR.
Kim, Jaehyun; Lee, Jae-Seung; Hwang, Taesoon; Lee, Soonchil
2004-01-01
A programmable quantum computer is experimentally demonstrated by nuclear magnetic resonance using one qubit for the program and two qubits for data. A non-separable two-qubit operation is performed in a programmable way to show the successful demonstration. Projective measurements required in the programmable quantum computer are simulated by averaging the results of experiments just like when producing an effective pure state.
Quantum Phase Transitions in Conventional Matrix Product Systems
Zhu, Jing-Min; Huang, Fei; Chang, Yan
2017-02-01
For matrix product states(MPSs) of one-dimensional spin-1/2 chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.
Hybird of Quantum Phases for Induced Dipole Moments
Ma, Kai
2016-01-01
The quantum phase effects for induced electric and magnetic dipole moments are investigated. It is shown that the phase shift received by induced electric dipole has the same form with the one induced by magnetic dipole moment, therefore the total phase is a hybrid of these two types of phase. This feature indicates that in order to have a decisive measurement on either one of these two phases, it is necessary to measure the velocity dependence of the observed phase.
Quantum charge pumps with topological phases in a Creutz ladder
Sun, Ning; Lim, Lih-King
2017-07-01
The quantum charge pumping phenomenon connects band topology through the dynamics of a one-dimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zak-phase difference of π and 2 π , respectively, various charge pumping schemes are studied by applying an elaborate Peierls phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This makes cold atoms with artificial gauge fields a unique system where this kind of phenomena can be realized.
Non-equilibrium quantum phase transition via entanglement decoherence dynamics
Lin, Yu-Chen; Yang, Pei-Yun; Zhang, Wei-Min
2016-01-01
We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained. PMID:27713556
Phase space picture of quantum mechanics group theoretical approach
Kim, Y S
1991-01-01
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.
Geometric phase in the G3+ quantum state evolution
Soiguine, Alexander
2015-01-01
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes explicitly defined as an arbitrary, variable plane in 3D. The result is that the quantum state definition and evolution receive more detailed description, including clear calculations of geometric phase, with important consequences for topological quantum computing.
Quantum decoherence of subcritical bubble in electroweak phase transition
Shiromizu, T
1995-01-01
In a weakly first order phase transition the typical scale of a subcritical bubble calculated in our previous papers turned out to be too small. At this scale quantum fluctuations may dominate and our previous classical result may be altered. So we examine the critical size of a subcritical bubble where quantum-to-classical transition occurs through quantum decoherence. We show that this critical size is almost equal to the typical scale which we previously obtained.
Quantum and Classical Phase Space Separability and Entanglement
Patwardhan, A
2002-01-01
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The correspondence between the classical and the quantum criterion of separability for the system is obtained in terms of these functions. Entanglement is generic and separability is special. Some applications are discussed in commonly occuring examples and possibly in exotic systems.
Observability of relative phases of macroscopic quantum states
Pati, A K
1998-01-01
After a measurement, to observe the relative phases of macroscopically distinguishable states we have to ``undo'' a quantum measurement. We generalise an earlier model of Peres from two state to N-state quantum system undergoing measurement process and discuss the issue of observing relative phases of different branches. We derive an inequality which is satisfied by the relative phases of macroscopically distinguishable states and consequently any desired relative phases can not be observed in interference setups. The principle of macroscopic complementarity is invoked that might be at ease with the macroscopic world. We illustrate the idea of limit on phase observability in Stern-Gerlach measurements and the implications are discussed.
Quantum Theory of Reactive Scattering in Phase Space
Goussev, A.; Schubert, R.; Waalkens, H.; Wiggins, S.; Nicolaides, CA; Brandas, E
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of Poincare-Birkhoff normal form theory and the perspective of dynamical systems theory. Over the past 10 years the classical normal form theory has provided a met
An extended phase-space SUSY quantum mechanics
Ter-Kazarian, G.
2009-01-01
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N
Quantum phase transition of a magnet in a spin bath
DEFF Research Database (Denmark)
Rønnow, H.M.; Parthasarathy, R.; Jensen, J.;
2005-01-01
The excitation spectrum of a model magnetic system, LiHoF(4), was studied with the use of neutron spectroscopy as the system was tuned to its quantum critical point by an applied magnetic field. The electronic mode softening expected for a quantum phase transition was forestalled by hyperfine...
An extended phase-space SUSY quantum mechanics
Ter-Kazarian, G.
2009-01-01
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N
Phase-modulation transmission system for quantum cryptography.
Mérolla, J M; Mazurenko, Y; Goedgebuer, J P; Porte, H; Rhodes, W T
1999-01-15
We describe a new method for quantum key distribution that utilizes phase modulation of sidebands of modulation by use of integrated electro-optic modulators at the transmitting and receiving modules. The system is shown to produce constructive or destructive interference with unity visibility, which should allow quantum cryptography to be carried out with high flexibility by use of conventional devices.
Bialczak, R C; Hofheinz, M; Lenander, M; Lucero, E; Neeley, M; O'Connell, A D; Sank, D; Wang, H; Weides, M; Wenner, J; Yamamoto, T; Cleland, A N; Martinis, J M
2010-01-01
A major challenge in the field of quantum computing is the construction of scalable qubit coupling architectures. Here, we demonstrate a novel tuneable coupling circuit that allows superconducting qubits to be coupled over long distances. We show that the inter-qubit coupling strength can be arbitrarily tuned over nanosecond timescales within a sequence that mimics actual use in an algorithm. The coupler has a measured on/off ratio of 1000. The design is self-contained and physically separate from the qubits, allowing the coupler to be used as a module to connect a variety of elements such as qubits, resonators, amplifiers, and readout circuitry over long distances. Such design flexibility is likely to be essential for a scalable quantum computer.
The Phase Space Formulation of Time-Symmetric Quantum Mechanics
National Research Council Canada - National Science Library
Charlyne de Gosson; Maurice A. de Gosson
2015-01-01
Time-symmetric quantum mechanics can be described in the Weyl–Wigner–Moyal phase space formalism by using the properties of the cross-terms appearing in the Wigner distribution of a sum of states...
Integrability and Quantum Phase Transitions in Interacting Boson Models
Dukelsky, J; García-Ramos, J E; Pittel, S
2003-01-01
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
Linear optical quantum computing in a single spatial mode.
Humphreys, Peter C; Metcalf, Benjamin J; Spring, Justin B; Moore, Merritt; Jin, Xian-Min; Barbieri, Marco; Kolthammer, W Steven; Walmsley, Ian A
2013-10-11
We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.
Quantum Phase Transitions in Odd-Mass Nuclei
Leviatan, A; Iachello, F
2011-01-01
Quantum shape-phase transitions in odd-even nuclei are investigated in the framework of the interacting boson-fermion model. Classical and quantum analysis show that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially near the critical point. Experimental evidence for the occurrence of spherical to axially-deformed transitions in odd-proton nuclei Pm, Eu and Tb (Z=61, 63, 65) is presented.
Experimental quantum-enhanced estimation of a lossy phase shift
Kacprowicz, M; Wasilewski, W; Banaszek, K; Walmsley, I A
2009-01-01
When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate Heisenberg limit on precision, but at the same time are extremely fragile to losses. In contrast, we provide experimental evidence that appropriately engineered quantum states outperform both standard and N00N states in the precision of phase estimation when losses are present.
Quantum Correlations in Heisenberg XY Chain
Institute of Scientific and Technical Information of China (English)
ZHU Yin-Yan; ZHANG Yong
2013-01-01
Quantum correlations measured by quantum discord (QD),measurement-induced distance (MID),and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated.The effects of DM interaction and anisotropic on the three correlations are considered.Characteristics of various correlation measures for the two-qubit states are compared.The increasing Dz increases QD,MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD.The three quantum correlations are always existent at very high temperature.MID is always larger than QD,but there is no definite ordering between QD and GMQD.
Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography.
Bonk, F A; deAzevedo, E R; Sarthour, R S; Bulnes, J D; Freitas, J C C; Guimarães, A P; Oliveira, I S; Bonagamba, T J
2005-08-01
This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.
Del Duce, A; Bayvel, P
2009-01-01
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa algorithm investigating different strategies for obtaining short total computational times. We test two separate approaches based on using different sets of entangling gates with the shortest possible gate computation time which, however, does not introduce leakage of quantum information to the control particles. The first set exploits fast approximations of controlled-phase gates as entangling gates, while the other one a...
A precise error bound for quantum phase estimation.
Directory of Open Access Journals (Sweden)
James M Chappell
Full Text Available Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.
Institute of Scientific and Technical Information of China (English)
Xu Xiao-Bo; Liu Jin-Ming; Yu Peng-Fei
2008-01-01
Taking the intrinsic decoherence effect into account,this paper investigates the entanglement of a two-qubit anisotropic Heisenberg XY Z model in the presence of nonuniform external magnetic fields by employing the concurrence as entanglement measure.It is found that both the intrinsic decoherence and the anisotropy of the system give a significant suppression to the entanglement.Moreover it finds that the initial state of the system plays an important role in the time evolution of the entanglement,which means that the entanglement of the system is independent of the nonuniformity and uniformity of the magnetic field when the system is in the initial state |ψ(0)>=|00>and |ψ(0)>=m |01＞+n|10＞,respectively.
Quantum simulations in phase-space: from quantum optics to ultra-cold physics
Drummond, Peter D.; Chaturvedi, Subhash
2016-07-01
As a contribution to the international year of light, we give a brief history of quantum optics in phase-space, with new directions including quantum simulations of multipartite Bell violations, opto-mechanics, ultra-cold atomic systems, matter-wave Bell violations, coherent transport and quantum fluctuations in the early Universe. We mostly focus on exact methods using the positive-P representation, and semiclassical truncated Wigner approximations.
Characteristic parameters and dynamics of two-qubit system in self-assembled monolayers
Rinkevicius, Z; Tsifrinovich, V I; Tretiak, S; Rinkevicius, Zilvinas; Berman, Gennady P.; Tsifrinovich, Vladimir I.; Tretiak, Sergei
2004-01-01
We suggest the application of nitronylnitroxide substituted with methyl group and 2,2,6,6-tetramethylpiperidin organic radicals as 1/2-spin qubits for self-assembled monolayer quantum devices. We show that the oscillating cantilever driven adiabatic reversals technique can provide the read-out of the spin states. We compute components of the $g$-tensor and dipole-dipole interaction tensor for these radicals. We show that the delocalization of the spin in the radical may significantly influence the dipole-dipole interaction between the spins.
Quantum phase transitions with parity-symmetry breaking and hysteresis
Trenkwalder, A.; Spagnolli, G.; Semeghini, G.; Coop, S.; Landini, M.; Castilho, P.; Pezzè, L.; Modugno, G.; Inguscio, M.; Smerzi, A.; Fattori, M.
2016-09-01
Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models. Its observation in real systems is often hampered by finite temperatures and limited control of the system parameters. In this work we report, for the first time, the experimental observation of the full quantum phase diagram across a transition where the spatial parity symmetry is broken. Our system consists of an ultracold gas with tunable attractive interactions trapped in a spatially symmetric double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas spontaneously localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the study of quantum critical phenomena at finite temperature, the investigation of macroscopic quantum tunnelling of the order parameter in the hysteretic regime and the production of strongly quantum entangled states at critical points.
Tesch, Carmen M; de Vivie-Riedle, Regina
2004-12-22
The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.
Active phase compensation of quantum key distribution system
Institute of Scientific and Technical Information of China (English)
CHEN Wei; HAN ZhengFu; MO XiaoFan; XU FangXing; WEI Guo; GUO GuangCan
2008-01-01
Quantum key distribution (QKD) system must be robust enough in practical communication. Besides birefringence of fiber, system performance is notably affected by phase drift. The Faraday-Michelson QKD system can auto-compensate the birefringence of fiber, but phase shift is still a serious problem in its practical operation. In this paper, the major reason of phase drift and its effect on Faraday-Michel-son QKD system is analyzed and an effective active phase compensation scheme is proposed. By this means, we demonstrate a quantum key distribution system which can stably run over 37-km fiber in practical working condition with the long-time averaged quantum bit error rate of 1.59% and the stan-dard derivation of 0.46%. This result shows that the active phase compensation scheme is suitable to be used in practical QKD systems based on double asymmetric interferometers without additional de-vices and thermal controller.
Quantum Theory of Reactive Scattering in Phase Space
Goussev, Arseni; Waalkens, Holger; Wiggins, Stephen
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these phase space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schr\\"odinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the qu...
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Quantum potential and symmetries in extended phase space
Nasiri, S
2005-01-01
Here, we study the concept of the quantum potential using an extended phase space technique. It seems that, for a given potential, there exist an extended canonical transformation that removes the expression for quantum potential in dynamical equation. The situation, mathematically, is similar to the appearance of centrifugal potential in going from Cartesian to spherical coordinates that changes the physical potential to an effective one. As Examples, the cases of harmonic oscillator, particle in a box and hydrogen atom are worked out, where the quantum potential disappears from the Wigner equation as a possible representation of quantum mechanics in the phase space. This representation that keeps the Hamilton-Jacobi equation form invariant could be obtained by a particular extended canonical transformation on Sobouti-Nasiri equation in extended phase space.
Quantum like representation of aSpiral Phase Plate
Bovino, Fabio A
2011-01-01
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of lowering and raising operators of quantum field. The correctness of this representation is proved by obtaining the same results of the Paul's operator in the single mode limit and comparing the results of two particular problems solved both in the classical and quantum picture: the action of a Spiral Phase Plate on a Gaussian Beam (corresponding to the vacuum state of the two-dimensional harmonic oscillator) and on a off-axis Gaussian Beam (corresponding to the displaced vacuum state in quantum picture).
No-go theorem for passive single-rail linear optical quantum computing.
Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A
2013-01-01
Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.
Quantum Griffiths Phase Inside the Ferromagnetic Phase of Ni1 -xVx
Wang, Ruizhe; Gebretsadik, Adane; Ubaid-Kassis, Sara; Schroeder, Almut; Vojta, Thomas; Baker, Peter J.; Pratt, Francis L.; Blundell, Stephen J.; Lancaster, Tom; Franke, Isabel; Möller, Johannes S.; Page, Katharine
2017-06-01
We study by means of bulk and local probes the d -metal alloy Ni1 -xVx close to the quantum critical concentration, xc≈11.6 %, where the ferromagnetic transition temperature vanishes. The magnetization-field curve in the ferromagnetic phase takes an anomalous power-law form with a nonuniversal exponent that is strongly x dependent and mirrors the behavior in the paramagnetic phase. Muon spin rotation experiments demonstrate inhomogeneous magnetic order and indicate the presence of dynamic fluctuating magnetic clusters. These results provide strong evidence for a quantum Griffiths phase on the ferromagnetic side of the quantum phase transition.
Quantum steering without inequalities
Chen, Jing-Ling; Wu, Chunfeng; Su, Hong-Yi; Cabello, Adan; Kwek, L C; Oh, C H
2012-01-01
We show that, for any two-qubit state, quantum steering can be proven without testing the violation of steering inequalities. We show that steerability is proven if Bob's normalized conditional states after Alice's measurements are pure. This method, which may be seen as the quantum steering analog of Greenberger-Horne-Zeilinger-like tests of Bell nonlocality without Bell inequalities, offers advantages with respect to the existing methods for experimentally testing quantum steering.
Transmission Phase Through Two Quantum Dots Embedded in a Four-Terminal Quantum Ring
Sigrist, M.; Fuhrer, A; Ihn, T.; Ensslin, K.; Wegscheider, W.; Bichler, M.
2003-01-01
We use the Aharonov-Bohm effect in a four-terminal ring based on a Ga[Al]As heterostructure for the measurement of the relative transmission phase. In each of the two interfering paths we induce a quantum dot. The number of electrons in the two dots can be controlled independently. The transmission phase is measured as electrons are added to or taken away from the individual quantum dots.
Quantum phases of dipolar soft-core bosons
Grimmer, D.; Safavi-Naini, A.; Capogrosso-Sansone, B.; Söyler, Ş. G.
2014-10-01
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform path-integral quantum Monte Carlo simulations using the worm algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighbor interaction, supersolid phases are stabilized by doping the solids not only with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and we suggest experimental conditions under which the pair checkerboard phase can be observed.
Theoretical Proposals of Quantum Phase-slip Devices
Hriscu, A.M.
2012-01-01
This thesis describes a series of theoretical proposals of novel circuits that embed ultrathin superconducting nanowires with coherent quantum phase-slips (QPS). The motivation for our proposals is twofold: firstly, to facilitate unambiguous experimental verification of coherent phase-slips. Secondl
Quantum Monte Carlo simulation of topological phase transitions
Yamamoto, Arata; Kimura, Taro
2016-12-01
We study the electron-electron interaction effects on topological phase transitions by the ab initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
Quantum Monte Carlo simulation of topological phase transitions
Yamamoto, Arata
2016-01-01
We study the electron-electron interaction effects on topological phase transitions by the ab-initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
Phase space formalisms of quantum mechanics with singular kernel
Sala, P R; Muga, J G
1997-01-01
The equivalence of the Rivier-Margenau-Hill and Born-Jordan-Shankara phase space formalisms to the conventional operator approach of quantum mechanics is demonstrated. It is shown that in spite of the presence of singular kernels the mappings relating phase space functions and operators back and forth are possible.
Quantum phase transitions in Bose-Fermi systems
Petrellis, D; Iachello, F
2011-01-01
Quantum phase transitions in a system of N bosons with angular momentum L=0,2 (s,d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially the critical value of the control parameter at which the phase transition occurs. Experimental evidence for the U(5)-SU(3) (spherical to axially-deformed) transition in odd-even nuclei is presented.
Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions.
Schwandt, David; Alet, Fabien; Capponi, Sylvain
2009-10-23
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.
Quantum phase transition of the transverse-field quantum Ising model on scale-free networks
Yi, Hangmo
2015-01-01
I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ =6 , I obtain results that are consistent with the mean-field theory. For λ =4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ >5 , but it continuously deviates from the mean-field theory as λ becomes smaller.
Modulated phases of graphene quantum Hall polariton fluids
Pellegrino, Francesco M. D.; Giovannetti, Vittorio; MacDonald, Allan H.; Polini, Marco
2016-11-01
There is a growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime, in which electron-electron interactions are expected to play a pivotal role. Here, focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron-electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which is often at a characteristic wave vector of the order of the inverse magnetic length.
Spin dynamics and spin freezing at ferromagnetic quantum phase transitions
Schmakat, P.; Wagner, M.; Ritz, R.; Bauer, A.; Brando, M.; Deppe, M.; Duncan, W.; Duvinage, C.; Franz, C.; Geibel, C.; Grosche, F. M.; Hirschberger, M.; Hradil, K.; Meven, M.; Neubauer, A.; Schulz, M.; Senyshyn, A.; Süllow, S.; Pedersen, B.; Böni, P.; Pfleiderer, C.
2015-07-01
We report selected experimental results on the spin dynamics and spin freezing at ferromagnetic quantum phase transitions to illustrate some of the most prominent escape routes by which ferromagnetic quantum criticality is avoided in real materials. In the transition metal Heusler compound Fe2TiSn we observe evidence for incipient ferromagnetic quantum criticality. High pressure studies in MnSi reveal empirical evidence for a topological non-Fermi liquid state without quantum criticality. Single crystals of the hexagonal Laves phase compound Nb1- y Fe2+ y provide evidence of a ferromagnetic to spin density wave transition as a function of slight compositional changes. Last but not least, neutron depolarisation imaging in CePd1- x Rh x underscore evidence taken from the bulk properties of the formation of a Kondo cluster glass.
Berry phase jumps and giant nonreciprocity in Dirac quantum dots
Rodriguez-Nieva, Joaquin F.; Levitov, Leonid S.
2016-12-01
We predict that a strong nonreciprocity in the resonance spectra of Dirac quantum dots can be induced by the Berry phase. The nonreciprocity arises in relatively weak magnetic fields and is manifest in anomalously large field-induced splittings of quantum dot resonances which are degenerate at B =0 due to time-reversal symmetry. This exotic behavior, which is governed by field-induced jumps in the Berry phase of confined electronic states, is unique to quantum dots in Dirac materials and is absent in conventional quantum dots. The effect is strong for gapless Dirac particles and can overwhelm the B -induced orbital and Zeeman splittings. A finite Dirac mass suppresses the effect. The nonreciprocity, predicted for generic two-dimensional Dirac materials, is accessible through Faraday and Kerr optical rotation measurements and scanning tunneling spectroscopy.
Indian Academy of Sciences (India)
E K Bashkirov; M S Mastyugin
2015-01-01
Considering two artificial identical atoms interacting with two-mode thermal field through non-degenerate two-photon transitions, this paper studies the influence of atomic coherence and dipole–dipole interaction on the entanglement of two qubits. It is found that the entanglement is greatly enhanced by these mechanisms.
Mott glass phase in a diluted bilayer Heisenberg quantum antiferromagnet
Ma, Nv-Sen; Sandvik, Anders W.; Yao, Dao-Xin
2015-09-01
We use quantum Monte Carlo simulations to study a dimer-diluted S = 1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J1 and interlayer interaction J2. Below the classical percolation threshold pc, the system has three phases reachable by tuning the interaction ratio g = J2/J1: a Néel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g. The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T > 0; χu exp(-b/Tα) with α < 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O(3) universality class in 2+1 dimensions.
Realizing quantum controlled phase flip through cavity QED
Xiao, Yun-Feng; Lin, Xiu-Min; Gao, Jie; Yang, Yong; Han, Zheng-Fu; Guo, Guang-Can
2004-10-01
We propose a scheme to realize quantum controlled phase flip (CPF) between two rare-earth ions embedded in the respective microsphere cavity via interacting with a single-photon pulse in sequence. The numerical simulations illuminate that the CPF gate between ions is robust and scalable with extremely high fidelity and low error rate. Our scheme is more applicable than other schemes presented before based on current laboratory cavity-QED technology, and it is possible to be used as an applied unit gate in future quantum computation and quantum communication.
Realizing Quantum Controlled Phase Flip through Cavity-QED
Xiao, Y F; Gao, J; Yang, Y; Han, Z F; Guo, G C; Xiao, Yun-Feng; Lin, Xiu-Min; Gao, Jie; Yang, Yong; Han, Zheng-Fu; Guo, Guang-Can
2004-01-01
We propose a scheme to realize quantum controlled phase flip (CPF) between two rare earth ions embedded in respective microsphere cavity via interacting with a single-photon pulse in sequence. The numerical simulations illuminate that the CPF gate between ions is robust and scalable with extremely high fidelity and low error rate. Our scheme is more applicable than other schemes presented before based on current laboratory cavity-QED technology, and it is possible to be used as an applied unit gate in future quantum computation and quantum communication.
Topological Effects on Quantum Phase Slips in Superfluid Spin Transport
Kim, Se Kwon; Tserkovnyak, Yaroslav
2016-03-01
We theoretically investigate effects of quantum fluctuations on superfluid spin transport through easy-plane quantum antiferromagnetic spin chains in the large-spin limit. Quantum fluctuations result in the decaying spin supercurrent by unwinding the magnetic order parameter within the easy plane, which is referred to as phase slips. We show that the topological term in the nonlinear sigma model for the spin chains qualitatively differentiates the decaying rate of the spin supercurrent between the integer versus half-odd-integer spin chains. An experimental setup for a magnetoelectric circuit is proposed, in which the dependence of the decaying rate on constituent spins can be verified by measuring the nonlocal magnetoresistance.
Characterization of optical quantum circuits using resonant phase shifts
Poot, Menno
2016-01-01
We demonstrate that important information about linear optical circuits can be obtained through the phase shift induced by integrated optical resonators. As a proof of principle, the phase of an unbalanced Mach-Zehnder interferometer is determined. Then the method is applied to a complex optical circuit designed for linear optical quantum computation. In this controlled-NOT gate with qubit initialization and tomography stages, the relative phases are determined as well as the coupling ratios of its directional couplers.
Crystal Phase Quantum Well Emission with Digital Control.
Assali, S; Lähnemann, J; Vu, T T T; Jöns, K D; Gagliano, L; Verheijen, M A; Akopian, N; Bakkers, E P A M; Haverkort, J E M
2017-09-18
One of the major challenges in the growth of quantum well and quantum dot heterostructures is the realization of atomically sharp interfaces. Nanowires provide a new opportunity to engineer the band structure as they facilitate the controlled switching of the crystal structure between the zinc-blende (ZB) and wurtzite (WZ) phases. Such a crystal phase switching results in the formation of crystal phase quantum wells (CPQWs) and quantum dots (CPQDs). For GaP CPQWs, the inherent electric fields due to the discontinuity of the spontaneous polarization at the WZ/ZB junctions lead to the confinement of both types of charge carriers at the opposite interfaces of the WZ/ZB/WZ structure. This confinement leads to a novel type of transition across a ZB flat plate barrier. Here, we show digital tuning of the visible emission of WZ/ZB/WZ CPQWs in a GaP nanowire by changing the thickness of the ZB barrier. The energy spacing between the sharp emission lines is uniform and is defined by the addition of single ZB monolayers. The controlled growth of identical quantum wells with atomically flat interfaces at predefined positions featuring digitally tunable discrete emission energies may provide a new route to further advance entangled photons in solid state quantum systems.
Hexatic and Microemulsion Phases in the 2d Quantum Plasma
Clark, Bryan; Casula, Michele; Ceperley, David
2009-03-01
It has been long known that the two-dimensional one component plasma supports both a Wigner-crystal and liquid phase. Classically [1,2], it is known that a hexatic phase exists but it is not known how this hexatic phase extends into the quantum regime. Moreover, at low temperature, phenomenological arguments [3] from Jamei, et. al. suggest the existence of microemulsion phases including stripes and bubbles. We use diffusion and path integral Monte Carlo to map out this phase diagram. We are able to extend the hexatic phase into the quantum regime as well as quantify the nature of the defects and exponents in the long range quantum system. We also specify the the nature, extent and existence (or lack thereof) of the expected low-T microemulsion phases. [0pt] [1] Muto, S. & Aoki, H. Crystallization of a classical two-dimensional electron system: Positional and orientational orders. Phys. Rev. B 59, 14911(1999).[0pt] [2] He, W.J. et al. Phase transition in a classical two-dimensional electron system. Phys. Rev. B 68, 195104(2003).[0pt] [3] Jamei, R., Kivelson, S. & Spivak, B. Universal Aspects of Coulomb-Frustrated Phase Separation. Phys. Rev. Lett. 94, 056805-4(2005).
Phase-Space Noncommutative Quantum Cosmology
Bastos, Catarina; Dias, Nuno Costa; Prata, João Nuno
2007-01-01
We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do not commute. Through the ADM formalism, we obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system. The Seiberg-Witten map is used to transform the noncommutative equation into a commutative one, i.e. into an equation with commutative variables, which depend on the noncommutative parameters, $\\theta$ and $\\eta$. Numerical solutions are found both for the classical and the quantum formulations of the system. These solutions are used to characterize the dynamics and the state of the universe. From the classical solutions we obtain the behavior of quantities such as the volume expansion, the shear and the characteristic volume. However the analysis of these quantities does not lead to any restriction on the value of the noncommutative parameters, $\\theta$ and $\\...
Dissipation-driven quantum phase transitions in collective spin systems
Energy Technology Data Exchange (ETDEWEB)
Morrison, S [Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Parkins, A S [Department of Physics, University of Auckland, Private Bag 92019, Auckland (New Zealand)], E-mail: smor161@aucklanduni.ac.nz
2008-10-14
We consider two different collective spin systems subjected to strong dissipation-on the same scale as interaction strengths and external fields-and show that either continuous or discontinuous dissipative quantum phase transitions can occur as the dissipation strength is varied. First, we consider a well-known model of cooperative resonance fluorescence that can exhibit a second-order quantum phase transition, and analyse the entanglement properties near the critical point. Next, we examine a dissipative version of the Lipkin-Meshkov-Glick interacting collective spin model, where we find that either first- or second-order quantum phase transitions can occur, depending only on the ratio of the interaction and external field parameters. We give detailed results and interpretation for the steady-state entanglement in the vicinity of the critical point, where it reaches a maximum. For the first-order transition we find that the semiclassical steady states exhibit a region of bistability. (fast track communication)
Phase space view of quantum mechanical systems and Fisher information
Energy Technology Data Exchange (ETDEWEB)
Nagy, Á., E-mail: anagy@madget.atomki.hu
2016-06-17
Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Quantum Phase Analysis of Field-Free Molecular Alignment
Yun, Sang Jae; Lee, Jongmin; Nam, Chang Hee
2015-01-01
We present quantum mechanical explanations for unresolved phenomena observed in field-free molecular alignment by a femtosecond laser pulse. Quantum phase analysis of molecular rotational states reveals the physical origin of the following phenomena: strong alignment peaks appear periodically, and the temporal shape of each alignment peak changes in an orderly fashion depending on molecular species; the strongest alignment is not achieved at the first peak; the transition between aligned and anti-aligned states is very fast compared to the time scale of rotational dynamics. These features are understood in a unified way analogous to that describing a carrier-envelope-phase-stabilized mode-locked laser.
Anomalous phase shift in a twisted quantum loop
Energy Technology Data Exchange (ETDEWEB)
Taira, Hisao [Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628 (Japan); Shima, Hiroyuki, E-mail: taira@eng.hokudai.ac.j [Department of Applied Mathematics 3, LaCaN, Universitat Politecnica de Catalunya (UPC), Barcelona 08034 (Spain)
2010-09-03
The coherent motion of electrons in a twisted quantum ring is considered to explore the effect of torsion inherent to the ring. Internal torsion of the ring composed of helical atomic configuration yields a non-trivial quantum phase shift in the electrons' eigenstates. This torsion-induced phase shift causes novel kinds of persistent current flow and an Aharonov-Bohm-like conductance oscillation. The two phenomena can occur even when no magnetic flux penetrates inside the twisted ring, thus being in complete contrast with the counterparts observed in untwisted rings.
Quantum phase transition induced by real-space topology
Li, C.; Zhang, G.; Lin, S.; Song, Z.
2016-12-01
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Quantum phase transition induced by real-space topology.
Li, C; Zhang, G; Lin, S; Song, Z
2016-12-22
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions
Acevedo, Oscar L.; Rodriguez, Ferney J.; Quiroga, Luis; Johnson, Neil F.; Rey, Ana M.
2014-05-01
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.
Magnetic-field sensing with quantum error detection under the effect of energy relaxation
Matsuzaki, Yuichiro; Benjamin, Simon
2017-03-01
A solid state spin is an attractive system with which to realize an ultrasensitive magnetic field sensor. A spin superposition state will acquire a phase induced by the target field, and we can estimate the field strength from this phase. Recent studies have aimed at improving sensitivity through the use of quantum error correction (QEC) to detect and correct any bit-flip errors that may occur during the sensing period. Here we investigate the performance of a two-qubit sensor employing QEC and under the effect of energy relaxation. Surprisingly, we find that the standard QEC technique to detect and recover from an error does not improve the sensitivity compared with the single-qubit sensors. This is a consequence of the fact that the energy relaxation induces both a phase-flip and a bit-flip noise where the former noise cannot be distinguished from the relative phase induced from the target fields. However, we have found that we can improve the sensitivity if we adopt postselection to discard the state when error is detected. Even when quantum error detection is moderately noisy, and allowing for the cost of the postselection technique, we find that this two-qubit system shows an advantage in sensing over a single qubit in the same conditions.
Girdhar, Parth; Cavalcanti, Eric G.
2016-09-01
We derive an inequality that is necessary and sufficient to show Einstein-Podolsky-Rosen (EPR) steering in a scenario employing only correlations between two arbitrary dichotomic measurements on each party. Thus the inequality is a complete steering analogy of the Clauser-Horne-Shimony-Holt (CHSH) inequality, a generalization of the result of Cavalcanti et al. [E. G. Cavalcanti, C. J. Foster, M. Fuwa, and H. M. Wiseman, JOSA B 32, A74 (2015), 10.1364/JOSAB.32.000A74]. We show that violation of the inequality only requires measuring over equivalence classes of mutually unbiased measurements on the trusted party and that in fact assuming a general two-qubit system arbitrary pairs of distinct projective measurements at the trusted party are equally useful. Via this it is found that for a given state the maximum violation of our EPR-steering inequality is equal to that for the CHSH inequality, so all states that are EPR steerable with CHSH-type correlations are also Bell nonlocal.
Slater, Paul B
2010-01-01
We study the moments of probability distributions generated by certain determinantal functions of generic two-qubit density matrices (rho) with real entries over the associated nine-dimensional convex domain, assigned Hilbert-Schmidt measure. It is found that the mean of the (nonnegative) determinant |rho| is 1/2288, the mean of the determinant of the partial transpose |rho^{PT}|--negative values indicating entanglement--is -1/858, while the mean of the product of these two determinants is zero. We ascertain the exact values--also rational numbers--of the succeeding eight moments of |rho^{PT}|. At intermediate steps in the derivation of the m-th moment, rational functions C_{2 j}(m) emerge, yielding the coefficients of the 2j-th power of even polynomials of total degree 4 m. These functions possess poles at finite series of consecutive half-integers, and certain (trivial) roots at finite series of consecutive natural numbers. The (nontrivial) dominant roots of C_{2 j}(m) appear to converge to the same half-in...
Phase transition of light on complex quantum networks.
Halu, Arda; Garnerone, Silvano; Vezzani, Alessandro; Bianconi, Ginestra
2013-02-01
Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is nontrivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.
Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states
Yurischev, M. A.
2017-10-01
For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy S_{cond} as a function of measurement angle θ \\in [0,π /2]. Numerical calculations show that the function S_{cond}(θ ) for X states can have at most one local extremum in the open interval from zero to π /2 (unimodality property). If the extremum is a minimum, the quantum discord displays region with variable (state-dependent) optimal measurement angle θ ^*. Such θ -regions (phases, fractions) are very tiny in the space of X-state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval (0,π /2). It is remarkable that the maxima exist in surprisingly wide regions, and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum.
Slow phase relaxation as a route to quantum computing beyond the quantum chaos border
Flores, J.; Kun, S. Yu.; Seligman, T. H.
2005-07-01
We reveal that phase memory can be much longer than energy relaxation in systems with exponentially large dimensions of Hilbert space; this finding is documented by 50 years of nuclear experiments, though the information is somewhat hidden. For quantum computers Hilbert spaces of dimension 2100 or larger will be typical and therefore this effect may contribute significantly to reduce the problems of scaling of quantum computers to a useful number of qubits.
Phase-controlled entanglement in a quantum-beat laser: application to quantum lithography
Sete, Eyob A.; Dorfman, Konstantin E.; Dowling, Jonathan P.
2011-11-01
We study entanglement generation and control in a quantum-beat laser coupled to a two-mode squeezed vacuum reservoir. We show that the generated entanglement is robust against cavity losses and environmental decoherence and can be controlled by tuning the phases of the microwave and the squeezed input fields. Moreover, we discuss two-photon correlations, absorption and implementations in quantum optical lithography.
A concise treatise on quantum mechanics in phase space
Curtright, Thomas L; Zachos, Cosmas K
2014-01-01
This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density -- matrices in a special Weyl representation -- and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formula...
Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations
Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor
2016-06-01
Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.
Black holes as critical point of quantum phase transition.
Dvali, Gia; Gomez, Cesar
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.
Black holes as critical point of quantum phase transition
Energy Technology Data Exchange (ETDEWEB)
Dvali, Gia [Arnold Sommerfeld Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany); CERN, Theory Department, Geneva 23 (Switzerland); New York University, Department of Physics, Center for Cosmology and Particle Physics, New York, NY (United States); Gomez, Cesar [Arnold Sommerfeld Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Muenchen (Germany); Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM-CSIC, C-XVI, Madrid (Spain)
2014-02-15
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs. (orig.)
Characterizing quantum phase transitions by single qubit operations
Giampaolo, S M; De Siena, S
2006-01-01
We introduce observable quantities, borrowing from concepts of quantum information theory, for the characterization of quantum phase transitions in spin systems. These observables are uniquely defined in terms of single spin unitary operations. We define the energy gap between the ground state and the state produced by the action of a single-qubit local gate. We show that this static quantity involves only single-site expectations and two-point correlation functions on the ground state. We then discuss a dynamical local observable defined as the acceleration of quantum state evolution after performing an instaneous single-qubit perturbation on the ground state. This quantity involves three-point correlations as well. We show that both the static and the dynamical observables detect and characterize completely quantum critical points in a class of spin systems.
Black Holes as Critical Point of Quantum Phase Transition
Dvali, Gia
2014-01-01
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.
Black holes as critical point of quantum phase transition
Dvali, Gia; Gomez, Cesar
2014-02-01
We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.
Quantum information processing in phase space: A modular variables approach
Ketterer, A.; Keller, A.; Walborn, S. P.; Coudreau, T.; Milman, P.
2016-08-01
Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.
A study on quantum similarity in the phase space
Sellier, J. M.; Ivanova, D. Y.; Dimov, I.
2016-10-01
Quantum similarity represents an important concept in the context of many applied disciplines such as physical and quantum chemistry. Nowadays, two definitions exist based, respectively, on the real and the phase spaces. In this paper, we focus on the second one, which was presented recently, and investigate it. In particular, being its mathematical definition dependent on a given integer s, we study the influence of this parameter on the similarity between two systems. To keep this investigation comprehensible, while still meaningful, we focus on a very simple quantum system represented by a hydrogen atom in the ground and excited states corresponding to the quantum numbers (n , l , m) =(1 , 0 , 0) and (n , l , m) =(2 , 0 , 0) .
Quantum phase transition in a common metal.
Yeh, A; Soh, Yeong-Ah; Brooke, J; Aeppli, G; Rosenbaum, T F; Hayden, S M
2002-10-03
The classical theory of solids, based on the quantum mechanics of single electrons moving in periodic potentials, provides an excellent description of substances ranging from semiconducting silicon to superconducting aluminium. Over the last fifteen years, it has become increasingly clear that there are substances for which the conventional approach fails. Among these are certain rare earth compounds and transition metal oxides, including high-temperature superconductors. A common feature of these materials is complexity, in the sense that they have relatively large unit cells containing heterogeneous mixtures of atoms. Although many explanations have been put forward for their anomalous properties, it is still possible that the classical theory might suffice. Here we show that a very common chromium alloy has some of the same peculiarities as the more exotic materials, including a quantum critical point, a strongly temperature-dependent Hall resistance and evidence for a 'pseudogap'. This implies that complexity is not a prerequisite for unconventional behaviour. Moreover, it should simplify the general task of explaining anomalous properties because chromium is a relatively simple system in which to work out in quantitative detail the consequences of the conventional theory of solids.
Dynamic phase response and amplitude-phase coupling of self-assembled semiconductor quantum dots
Lingnau, Benjamin; Herzog, Bastian; Kolarczik, Mirco; Woggon, Ulrike; Lüdge, Kathy; Owschimikow, Nina
2017-06-01
The optical excitation of semiconductor gain media introduces both gain and refractive index changes, commonly referred to as amplitude-phase coupling. Quantum-confined structures with an energetically well separated carrier reservoir usually exhibit a decreased amplitude-phase coupling compared to bulk materials. However, its magnitude and definition is still controversially discussed. We investigate the fundamental processes influencing the amplitude-phase coupling in semiconductor quantum-dot media using a coupled-carrier rate-equation model. We are able to analyze the dependence on the electronic structure and suggest routes towards an optimization of the dynamic phase response of the gain material.
Emission energy control of semiconductor quantum dots using phase change material
Kanazawa, Shohei; Sato, Yu; Yamamura, Ariyoshi; Saiki, Toshiharu
2015-03-01
Semiconductor quantum dots have paid much attention as it is a promising candidate for quantum, optical devices, such as quantum computer and quantum dot laser. We propose a local emission energy control method of semiconductor quantum dots using applying strain by volume expansion of phase change material. Phase change material can change its phase crystalline to amorphous, and the volume expand by its phase change. This method can control energy shift direction and amount by amorphous religion and depth. Using this method, we matched emission energy of two InAs/InP quantum dots. This achievement can connect to observing superradiance phenomenon and quantum dot coupling effect.
Quantum Phase Transitions and Dimerized Phases in Frustrated Spin Ladder
Institute of Scientific and Technical Information of China (English)
WEN Rui; LIU Guang-Hua; TIAN Guang-Shan
2011-01-01
In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group (DMRG) algorithm. Effect of the intra-chain next-nearestneighbor (NNN) super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.
Quantum Networks with Chiral-Light-Matter Interaction in Waveguides
Mahmoodian, Sahand; Lodahl, Peter; Sørensen, Anders S.
2016-12-01
We propose a scalable architecture for a quantum network based on a simple on-chip photonic circuit that performs loss-tolerant two-qubit measurements. The circuit consists of two quantum emitters positioned in the arms of an on-chip Mach-Zehnder interferometer composed of waveguides with chiral-light-matter interfaces. The efficient chiral-light-matter interaction allows the emitters to perform high-fidelity intranode two-qubit parity measurements within a single chip and to emit photons to generate internode entanglement, without any need for reconfiguration. We show that, by connecting multiple circuits of this kind into a quantum network, it is possible to perform universal quantum computation with heralded two-qubit gate fidelities F ˜0.998 achievable in state-of-the-art quantum dot systems.
Quantum computation architecture using optical tweezers
DEFF Research Database (Denmark)
Weitenberg, Christof; Kuhr, Stefan; Mølmer, Klaus;
2011-01-01
We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits...... quantum computing....
Auto-compensating differential phase shift quantum key distribution
Han, X; Zhou, C; Zeng, H; Han, Xiaohong; Wu, Guang; Zhou, Chunyuan; Zeng, Heping
2005-01-01
We propose an auto-compensating differential phase shift scheme for quantum key distribution with a high key-creation efficiency, which skillfully makes use of automatic alignment of the photon polarization states in optical fiber with modified Michelson interferometers composed of unequal arms with Faraday mirrors at the ends. The Faraday-mirrors-based Michelson interferometers not only function as pulse splitters, but also enable inherent compensation of polarization mode dispersion in the optic-fiber paths at both Alice's and Bob's sites. The sequential pulses encoded by differential phase shifts pass through the quantum channel with the same polarization states, resulting in a stable key distribution immune to the polarization mode dispersion in the quantum channel. Such a system features perfect stability and higher key creation efficiency over traditional schemes.
Emergence of coherence and the dynamics of quantum phase transitions
Braun, Simon; Friesdorf, Mathis; Hodgman, Sean S.; Schreiber, Michael; Ronzheimer, Jens Philipp; Riera, Arnau; del Rey, Marco; Bloch, Immanuel; Eisert, Jens
2015-01-01
The dynamics of quantum phase transitions pose one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition. In the 1D Bose–Hubbard model, we find perfect agreement between experimental observations and numerical simulations for the resulting coherence length. We, thereby, perform a largely certified analog quantum simulation of this strongly correlated system reaching beyond the regime of free quasiparticles. Experimentally, we additionally explore the emergence of coherence in higher dimensions, where no classical simulations are available, as well as for negative temperatures. For intermediate quench velocities, we observe a power-law behavior of the coherence length, reminiscent of the Kibble–Zurek mechanism. However, we find nonuniversal exponents that cannot be captured by this mechanism or any other known model. PMID:25775515
Benford's Law: Detection of Quantum Phase Transitions similarly as Earthquakes
De, Aditi Sen
2011-01-01
More than a century earlier, it was predicted that the first significant digit appearing in a data, be it from natural sciences or from some mathematical series, will be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benford's law. It has been observed to hold for data from a huge variety of sources, ranging from earthquakes to infectious disease cases. Quantum phase transitions are cooperative phenomena where qualitative changes occur in physical quantities of a many-body system at zero temperature. We find that Benford's law can be applied to detect quantum phase transitions in a way that is very similar to how it can distinguish earthquakes from background noise. Being certainly of very different physical origins, seismic activity and quantum cooperative phenomena may therefore be detected by similar methods. The result may provide methods to overcome the limitations associated with precise measurements in experiments.
Scaling and Universality at Dynamical Quantum Phase Transitions.
Heyl, Markus
2015-10-02
Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices
Wellard, C J; Wellard, Cameron; Orus, Roman
2004-01-01
Motivated by its relation to an NP-hard problem we analyze the ground state properties of anti-ferromagnetic Ising-spin networks in planar cubic lattices under the action of homogeneous transverse and longitudinal magnetic fields. We consider different instances of the cubic geometry and find a set of quantum phase transitions for each one of the systems, which we characterize by means of entanglement behavior and majorization theory. Entanglement scaling at the critical region is in agreement with results arising from conformal symmetry, therefore even the simplest planar systems can display very large amounts of quantum correlation. No conclusion can be made as to the scaling behavior of the minimum energy gap, with the data allowing equally good fits to exponential and power law decays. Analysis of entanglement and especially of majorization instead of the energy spectrum proves to be a good way of detecting quantum phase transitions in highly frustrated configurations.
Research on Quantum Searching Algorithms Based on Phase Shifts
Institute of Scientific and Technical Information of China (English)
ZHONG Pu-Cha; BAO Wan-Su
2008-01-01
@@ One iterative in Grover's original quantum search algorithm consists of two Hadamard-Walsh transformations, a selective amplitude inversion and a diffusion amplitude inversion. We concentrate on the relation among the probability of success of the algorithm, the phase shifts, the number of target items and the number of iterations via replacing the two amplitude inversions by phase shifts of an arbitrary φ = ψ(0 ≤φ, ψ≤ 2π). Then, according to the relation we find out the optimal phase shifts when the number of iterations is given. We present a new quantum search algorithm based on the optimal phase shifts of 1.018 after 0.5π /√M/N iterations. The new algorithm can obtain either a single target item or multiple target items in the search space with the probability of success at least 93.43%.
Quantum phase transitions in the noncommutative Dirac Oscillator
Panella, O
2014-01-01
We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical value ($B_{\\text{cr}}$) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); $ii$) non-commutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\\text{cr}}^*$, where there is a second quantum phase transition (right-left), --this critical point disappears in the commutative limit--. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed.
Cavity-assisted dynamical quantum phase transition in superconducting quantum simulators
Tian, Lin
Coupling a quantum many-body system to a cavity can create bifurcation points in the phase diagram, where the many-body system switches between different phases. Here I will discuss the dynamical quantum phase transitions at the bifurcation points of a one-dimensional transverse field Ising model coupled to a cavity. The Ising model can be emulated with various types of superconducting qubits connected in a chain. With a time-dependent Bogoliubov method, we show that an infinitesimal quench of the driving field can cause gradual evolution of the transverse field on the Ising spins to pass through the quantum critical point. Our calculation shows that the cavity-induced nonlinearity plays an important role in the dynamics of this system. Quasiparticles can be excited in the Ising chain during this process, which results in the deviation of the system from its adiabatic ground state. This work is supported by the National Science Foundation under Award Number 0956064.
Partial dynamical symmetry at critical points of quantum phase transitions.
Leviatan, A
2007-06-15
We show that partial dynamical symmetries can occur at critical points of quantum phase transitions, in which case underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several types of partial dynamical symmetries are demonstrated with the example of critical-point Hamiltonians for first- and second-order transitions in the framework of the interacting boson model, whose dynamical symmetries correspond to different shape phases in nuclei.
Divergent thermopower without a quantum phase transition.
Limtragool, Kridsanaphong; Phillips, Philip W
2014-08-22
A general principle of modern statistical physics is that divergences of either thermodynamic or transport properties are only possible if the correlation length diverges. We show by explicit calculation that the thermopower in the quantum XY model d = 1 + 1 and the Kitaev model in d = 2 + 1 can (i) diverge even when the correlation length is finite and (ii) remain finite even when the correlation length diverges, thereby providing a counterexample to the standard paradigm. Two conditions are necessary: (i) the sign of the charge carriers and that of the group velocity must be uncorrelated and (ii) the current operator defined formally as the derivative of the Hamiltonian with respect to the gauge field does not describe a set of excitations that have a particle interpretation, as in strongly correlated electron matter. Recent experimental and theoretical findings on the divergent thermopower of a 2D electron gas are discussed in this context.
Quantum Shape-Phase Transitions in Finite Nuclei
Leviatan, A
2007-01-01
Quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Critical-point Hamiltonians for first- and second-order transitions are identified by resolving them into intrinsic and collective parts. Suitable wave functions and finite-N estimates for observables at the critical-points are derived.
Quantum Shape-Phase Transitions in Finite Nuclei
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)
2007-05-15
Quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Critical-point Hamiltonians for first- and second-order transitions are identified by resolving them into intrinsic and collective parts. Suitable wave functions and finite-N estimates for observables at the critical-points are derived.
Quantum phase transitions in low-dimensional optical lattices
Di Liberto, M.F.
2015-01-01
In this thesis, we discuss quantum phase transitions in low-dimensional optical lattices, namely one- and two-dimensional lattices. The dimensional confinement is realized in experiments by suppressing the hopping in the extra dimensions through a deep potential barrier that prevents the atoms to tu
Angular Momentum Phase State Representation for Quantum Pendulum
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; WANG Ji-Suo
2005-01-01
To consummate the quantum pendulum theory whose Hamiltonian takes bosonic operator formalism and manifestly exhibits its dynamic behaviour in the entangled state representation, we introduce angular momentum state representation and phase state representation. It turns out that the angular momentum state is the partial wave expansion of the entangled state.
Deformation quantization: Quantum mechanics lives and works in phase space
Directory of Open Access Journals (Sweden)
Zachos Cosmas K.
2014-01-01
A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002, and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014.
Iterative Phase Optimization of Elementary Quantum Error Correcting Codes
Müller, M.; Rivas, A.; Martínez, E. A.; Nigg, D.; Schindler, P.; Monz, T.; Blatt, R.; Martin-Delgado, M. A.
2016-07-01
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.
An ultrafast quantum random number generator based on quantum phase fluctuations
Xu, Feihu; Ma, Xiongfeng; Xu, He; Zheng, Haoxuan; Lo, Hoi-Kwong
2012-01-01
A quantum random number generator (QRNG) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics. Most approaches to QRNG employ single-photon detection technologies and are limited in speed. Here, we propose and experimentally demonstrate an ultrafast QRNG at a rate over 6 Gb/s based on the quantum phase fluctuations of a laser operating near threshold. Moreover, we consider a potential adversary who has partial knowledge on the raw data and discuss how one can rigorously remove such partial knowledge with post-processing. We quantify the quantum randomness through min-entropy by modeling our system, and employ two extractors, Trevisan's extractor and Toeplitz-hashing, to distill the randomness, which is information-theoretically provable. The simplicity and high-speed of our experimental setup show the feasibility of a robust, low-cost, high-speed QRNG.
Quantum superposition of localized and delocalized phases of photons
Wu, Chun-Wang; Deng, Zhi-Jiao; Dai, Hong-Yi; Chen, Ping-Xing; Li, Cheng-Zu
2011-01-01
Based on a variant of 2-site Jaynes-Cummings-Hubbard model, which is constructed using superconducting circuits, we propose a method to coherently superpose the localized and delocalized phases of photons. In our model, two nonlinear superconducting stripline resonators are coupled by an interfacial circuit composed of parallel combination of a superconducting qubit and a capacitor, which plays the role of a quantum knob for the photon hopping rate: with the knob qubit in its ground/excited state, the injected photons tend to be localized/delocalized in the resonators. We show that, by applying a microwave field with appropriate frequency on the knob qubit, we could demonstrate Rabi oscillation between photonic localized phase and delocalized phase. Furthermore, this set-up offers advantages (e. g. infinite on/off ratio) over other proposals for the realization of scalable quantum computation with superconducting qubits.
Quantum Nucleation of Phase Slips in 1-d Superfluids
Arovas, Daniel
1998-03-01
The rate for quantum nucleation of phase slips past an impurity in a one-dimensional superfluid is computed. Real time evolution of the nonlinear Schrödinger equation shows that there is a critical velocity vc below which solutions are time-independent [1,2]; this is the regime of quantum phase slip nucleation. We start with the Gross-Pitaevskii model in the presence of an impurity potential, and derive the Euclidean action for a space-time vortex-antivortex pair, which describes a phase slip event. The action is computed as a function of the superfluid velocity v and the impurity potential width and depth.l [1] V. Hakim, Phys. Rev. E 55, 2835 (1997).l [1] J. A. Freire, D. P. Arovas, and H. Levine, Phys. Rev. Lett (in press, 1997).l
An extended phase-space SUSY quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ter-Kazarian, G [Byurakan Astrophysical Observatory, Byurakan 378433, Aragatsotn District (Armenia)], E-mail: gago_50@yahoo.com
2009-02-06
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.
Memory cost of quantum contextuality
Kleinmann, Matthias; Portillo, José R; Larsson, Jan-Åke; Cabello, Adán
2010-01-01
The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to understand the difference between quantum and classical physics. We investigate the minimum classical memory needed to simulate the phenomenon of state-independent quantum contextuality in sequential measurements. We derive optimal simulation strategies for several important cases and prove that two bits of classical memory do not suffice to reproduce the results of sequential measurements on a two-qubit system.
Wave mechanics in quantum phase space: hydrogen atom
Institute of Scientific and Technical Information of China (English)
LU Jun
2007-01-01
The rigorous sohutions of the stationary Schr(o)dinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The "Fourier-like"projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.
Quantum superposition of localized and delocalized phases of photons
Energy Technology Data Exchange (ETDEWEB)
Wu, Chun-Wang, E-mail: cwwu@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China); Gao, Ming; Deng, Zhi-Jiao; Dai, Hong-Yi; Chen, Ping-Xing; Li, Cheng-Zu [College of Science, National University of Defense Technology, Changsha 410073 (China)
2012-09-10
Based on a variant of 2-site Jaynes–Cummings–Hubbard model constructed using superconducting circuits, we propose a method to coherently superpose the localized and delocalized phases of microwave photons, which makes it possible to engineer the collective features of multiple photons in the quantum way using an individual two-level system. Our proposed architecture is also a promising candidate for implementing distributed quantum computation since it is capable of coupling remote qubits in separate resonators in a controllable way. -- Highlights: ► A method to coherently superpose the different photonic states is proposed. ► The used Jaynes–Cummings model can be constructed using superconducting circuits. ► This model can be also used for distributed quantum computation.
Lyapunov exponent in quantum mechanics A phase-space approach
Man'ko, V I
2000-01-01
Using the symplectic tomography map, both for the probability distributionsin classical phase space and for the Wigner functions of its quantumcounterpart, we discuss a notion of Lyapunov exponent for quantum dynamics.Because the marginal distributions, obtained by the tomography map, are alwayswell defined probabilities, the correspondence between classical and quantumnotions is very clear. Then we also obtain the corresponding expressions inHilbert space. Some examples are worked out. Classical and quantum exponentsare seen to coincide for local and non-local time-dependent quadraticpotentials. For non-quadratic potentials classical and quantum exponents aredifferent and some insight is obtained on the taming effect of quantummechanics on classical chaos. A detailed analysis is made for the standard map.Providing an unambiguous extension of the notion of Lyapunov exponent toquantum mechnics, the method that is developed is also computationallyefficient in obtaining analytical results for the Lyapunov expone...
Aspects of Phase-Space Noncommutative Quantum Mechanics
Bertolami, O
2015-01-01
In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP) in the context of the gravitational quantum well (GQW) are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative set up, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.
Aspects of phase-space noncommutative quantum mechanics
Directory of Open Access Journals (Sweden)
O. Bertolami
2015-11-01
Full Text Available In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP in the context of the gravitational quantum well (GQW are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative setup, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.
Robust guaranteed-cost adaptive quantum phase estimation
Roy, Shibdas; Berry, Dominic W.; Petersen, Ian R.; Huntington, Elanor H.
2017-05-01
Quantum parameter estimation plays a key role in many fields like quantum computation, communication, and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model. Any inevitable uncertainty in the model parameters may heavily degrade the quality of the estimate. It is therefore desired to make the estimation process robust to such uncertainties. Robust estimation was previously studied for a varying phase, where the goal was to estimate the phase at some time in the past, using the measurement results from both before and after that time within a fixed time interval up to current time. Here, we consider a robust guaranteed-cost filter yielding robust estimates of a varying phase in real time, where the current phase is estimated using only past measurements. Our filter minimizes the largest (worst-case) variance in the allowable range of the uncertain model parameter(s) and this determines its guaranteed cost. It outperforms in the worst case the optimal Kalman filter designed for the model with no uncertainty, which corresponds to the center of the possible range of the uncertain parameter(s). Moreover, unlike the Kalman filter, our filter in the worst case always performs better than the best achievable variance for heterodyne measurements, which we consider as the tolerable threshold for our system. Furthermore, we consider effective quantum efficiency and effective noise power, and show that our filter provides the best results by these measures in the worst case.
Manu, V S
2011-01-01
An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally veri?ed by a NMR quantum information processor. The procedure is scalable and can be applied to any set of orthogonal states. Scalability is demonstrated through Matlab simulation.
Quantum geometry from phase space reduction
Conrady, Florian
2009-01-01
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin--Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the FK spin foam model as an integral over classical tetrahedra and the asymptotics of the vertex amplitude is determined.
A Quantum Phase Transition in the Cosmic Ray Energy Distribution
Widom, A; Srivastava, Y
2015-01-01
We here argue that the "knee" of the cosmic ray energy distribution at $E_c \\sim 1$ PeV represents a second order phase transition of cosmic proportions. The discontinuity of the heat capacity per cosmic ray particle is given by $\\Delta c=0.450196\\ k_B$. However the idea of a deeper critical point singularity cannot be ruled out by present accuracy in neither theory nor experiment. The quantum phase transition consists of cosmic rays dominated by bosons for the low temperature phase E E_c$. The low temperature phase arises from those nuclei described by the usual and conventional collective boson models of nuclear physics. The high temperature phase is dominated by protons. The transition energy $E_c$ may be estimated in terms of the photo-disintegration of nuclei.
Pairwise Quantum Correlations for Superpositions of Dicke States
Institute of Scientific and Technical Information of China (English)
席政军; 熊恒娜; 李永明; 王晓光
2012-01-01
Pairwise correlation is really an important property for multi-qubit states.For the two-qubit X states extracted from Dicke states and their superposition states,we obtain a compact expression of the quantum discord by numerical check.We then apply the expression to discuss the quantum correlation of the reduced two-qubit states of Dicke states and their superpositions,and the results are compared with those obtained by entanglement of formation,which is a quantum entanglement measure.
Measurement of Quantum Phase-Slips in Josephson Junction Chains
Guichard, Wiebke
2011-03-01
Quantum phase-slip dynamics in Josephson junction chains could provide the basis for the realization of a new type of topologically protected qubit or for the implementation of a new current standard. I will present measurements of the effect of quantum phase-slips on the ground state of a Josephson junction chain. We can tune in situ the strength of the phase-slips. These phase-slips are the result of fluctuations induced by the finite charging energy of each junction in the chain. Our measurements demonstrate that a Josephson junction chain under phase bias constraint behaves in a collective way. I will also show evidence of coherent phase-slip interference, the so called Aharonov-Casher effect. This phenomenon is the dual of the well known Aharonov-Bohm interference. In collaboration with I.M. Pop, Institut Neel, C.N.R.S. and Universite Joseph Fourier, BP 166, 38042 Grenoble, France; I. Protopopov, L. D. Landau Institute for Theoretical Physics, Kosygin str. 2, Moscow 119334, Russia and Institut fuer Nanotechnologie, Karlsruher Institut fuer Technologie, 76021 Karlsruhe, Germany; and F. Lecocq, Z. Peng, B. Pannetier, O. Buisson, Institut Neel, C.N.R.S. and Universite Joseph Fourier. European STREP MIDAS, ANR QUANTJO.
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Excited-state quantum phase transition in the Rabi model
Puebla, Ricardo; Hwang, Myung-Joong; Plenio, Martin B.
2016-08-01
The Rabi model, a two-level atom coupled to a harmonic oscillator, can undergo a second-order quantum phase transition (QPT) [M.-J. Hwang et al., Phys. Rev. Lett. 115, 180404 (2015), 10.1103/PhysRevLett.115.180404]. Here we show that the Rabi QPT accompanies critical behavior in the higher-energy excited states, i.e., the excited-state QPT (ESQPT). We derive analytic expressions for the semiclassical density of states, which show a logarithmic divergence at a critical energy eigenvalue in the broken symmetry (superradiant) phase. Moreover, we find that the logarithmic singularities in the density of states lead to singularities in the relevant observables in the system such as photon number and atomic polarization. We corroborate our analytical semiclassical prediction of the ESQPT in the Rabi model with its numerically exact quantum mechanical solution.
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-01
The quantum versions of de Finetti’s theorem derived so far express the convergence of n -partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ⊗n . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n -mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Geometric quantum phase in the spacetime of topological defects
Energy Technology Data Exchange (ETDEWEB)
Bakke, K [Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU (United Kingdom); Furtado, C; Nascimento, J R [Departamento de Fisica, Universidade Federal da ParaIba, Caixa Postal 5008, 58051-970, Joao Pessoa, PB (Brazil)
2011-07-08
In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
Geometric quantum phase in the spacetime of topological defects
Bakke, K.; Furtado, C.; Nascimento, J. R.
2011-07-01
In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
Efficient quantum walk on a quantum processor
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.
2016-05-01
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.
Efficient quantum walk on a quantum processor.
Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L; Wang, Jingbo B; Matthews, Jonathan C F
2016-05-05
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.
Quantum information entropy for one-dimensional system undergoing quantum phase transition
Xu-Dong, Song; Shi-Hai, Dong; Yu, Zhang
2016-05-01
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic “Landau” potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy Sx and the momentum entropy Sp at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition. Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.
Intrinsic Spin Hall Effect Induced by Quantum Phase Transition in HgCdTe Quantum Wells
Energy Technology Data Exchange (ETDEWEB)
Yang, Wen; Chang, Kai; /Beijing, Inst. Semiconductors; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
Spin Hall effect can be induced both by the extrinsic impurity scattering and by the intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. This difference gives a direct mechanism to experimentally distinguish the intrinsic spin Hall effect from the extrinsic one.
The Quantum Space Phase Transitions for Particles and Force Fields
Chung D.-Y.; Krasnoholovets V.
2006-01-01
We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment spac...
Berry phase, topology, and degeneracies in quantum nanomagnets.
Bruno, Patrick
2006-03-24
A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.
Quantum phase diagram of Polar Molecules in 1D Double Wire Systems
Chang, Chi-Ming; Wang, Daw-Wei
2007-03-01
We study the quantum phase transitions of fermionic polar molecules loaded in a double wire potential. By tuning the magnitude and direction of external electric field we observed many interesting quantum phases in different parameter range, including an easy-plane spin density wave, a triplet superconducting phase, and a truly long range order of easy-axis ferromagnetic phase in strong interacting regime. We also discuss how these exotic quantum phases can be measured in the existing experimental techniques.
Chang, Cui-Zu; Zhao, Weiwei; Li, Jian; Jain, J. K.; Liu, Chaoxing; Moodera, Jagadeesh S.; Chan, Moses H. W.
2016-09-01
Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in the quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. We expect that our work will motivate much further investigation of many properties of quantum phase transition in this new context.
Duality, Phase Structures and Dilemmas in Symmetric Quantum Games
Ichikawa, T; Ichikawa, Tsubasa; Tsutsui, Izumi
2006-01-01
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of...
The Quantum Space Phase Transitions for Particles and Force Fields
Directory of Open Access Journals (Sweden)
Chung D.-Y.
2006-07-01
Full Text Available We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separat continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a "hedge boson force field", consisting of a "vacuum" core surrounded by a hedge boson shell, like a bubble with boundary.
Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems
Heiss, W D; Rotter, I
1998-01-01
Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.
Quantum phase transition between cluster and antiferromagnetic states
Son, Wonmin; Fazio, Rosario; Hamma, Alioscia; Pascazio, Saverio; Vedral, Vlatko
2011-01-01
We study a Hamiltonian system describing a three spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied. Our findings in one dimension corroborate the analysis of the two dimensional generalization of the system, indicating, at a mean field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.
Reference frame independent quantum key distribution
Laing, Anthony; Rarity, John G; O'Brien, Jeremy L
2010-01-01
We describe a quantum key distribution protocol based on pairs of entangled qubits that generates a secure key between two partners in an environment of unknown and slowly varying reference frame. A direction of particle delivery is required, but the phases between the computational basis states need not be known or fixed. The protocol can simplify the operation of existing setups and has immediate applications to emerging scenarios such as earth-to-satellite links and the use of integrated photonic waveguides. We compute the asymptotic secret key rate for a two-qubit source, which coincides with the rate of the six-state protocol for white noise. We give the generalization of the protocol to higher-dimensional systems and detail a scheme for physical implementation in the three dimensional qutrit case.
Topological phases and transport properties of screened interacting quantum wires
Xu, Hengyi; Xiong, Ye; Wang, Jun
2016-10-01
We study theoretically the effects of long-range and on-site Coulomb interactions on the topological phases and transport properties of spin-orbit-coupled quasi-one-dimensional quantum wires imposed on a s-wave superconductor. The distributions of the electrostatic potential and charge density are calculated self-consistently within the Hartree approximation. Due to the finite width of the wires and charge repulsion, the potential and density distribute inhomogeneously in the transverse direction and tend to accumulate along the lateral edges where the hard-wall confinement is assumed. This result has profound effects on the topological phases and the differential conductance of the interacting quantum wires and their hybrid junctions with superconductors. Coulomb interactions renormalize the gate voltage and alter the topological phases strongly by enhancing the topological regimes and producing jagged boundaries. Moreover, the multicritical points connecting different topological phases are modified remarkably in striking contrast to the predictions of the two-band model. We further suggest the possible non-magnetic topological phase transitions manipulated externally with the aid of long-range interactions. Finally, the transport properties of normal-superconductor junctions are further examined, in particular, the impacts of Coulomb interactions on the zero-bias peaks related to the Majorana fermions and near zero-energy peaks.
Quantum and thermal phase escape in extended Josephson systems
Energy Technology Data Exchange (ETDEWEB)
Kemp, A.
2006-07-12
In this work I examine phase escape in long annular Josephson tunnel junctions. The sine-Gordon equation governs the dynamics of the phase variable along the junction. This equation supports topological soliton solutions, which correspond to quanta of magnetic flux trapped in the junction barrier. For such Josephson vortices an effective potential is formed by an external magnetic field, while a bias current acts as a driving force. Both together form a metastable potential well, which the vortex is trapped in. When the driving force exceeds the pinning force of the potential, the vortex escapes and the junction switches to the voltage state. At a finite temperature the driving force fluctuates. If the junction's energy scale is small, the phase variable can undergo a macroscopic quantum tunneling (MQT) process at temperatures below the crossover temperature. Without a vortex trapped, the metastable state is not a potential minimum in space, but a potential minimum at zero phase difference. (orig.)
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, David; Qian, Dong; Wray, Lewis; Xia, Yuqi; San Hor, Yew; Cava, Robert; Hasan, Zahid
2009-03-01
When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin orbit interactions may also naturally support conducting topological boundary states in the quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields. Bulk Bi1-xSbx single crystals are predicted to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy, we report the direct observation of massive Dirac particles in the bulk of Bi0.9Sb0.1 and provide a comprehensive mapping of the Dirac insulators gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the topological metal.
An introduction to the tomographic picture of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ibort, A [Departamento de Matematicas, Universidad Carlos III de Madrid, Avda de la Universidad 30, 28911 Leganes, Madrid (Spain); Man' ko, V I [P N Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G; Simoni, A; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S Angelo, via Cintia, 80126 Naples (Italy)], E-mail: albertoi@math.uc3m.es, E-mail: manko@na.infn.it, E-mail: marmo@na.infn.it, E-mail: simoni@na.infn.it, E-mail: ventriglia@na.infn.it
2009-06-15
Starting from the famous Pauli problem on the possibility of associating quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference between those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to non-negativity of probability density on phase space in the classical domain. The intersection of such sets is studied. The mathematical mechanism that allows us to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc is clarified and a connection with abstract Hilbert space properties is established. The superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equations like quantum evolution and energy spectra equations are given in an explicit form. A method to check experimentally the uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two-qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.
Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
Bhattacharya, Utso; Dutta, Amit
2017-07-01
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016), 10.1103/PhysRevB.93.085416] for one-dimensional situations. This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.
Control of the spin geometric phase in semiconductor quantum rings
Nagasawa, Fumiya; Frustaglia, Diego; Saarikoski, Henri; Richter, Klaus; Nitta, Junsaku
2013-09-01
Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov-Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations.
A study of Quantum Correlations in Open Quantum Systems
Chakrabarty, Indranil; Siddharth, Nana
2010-01-01
In this work, we study quantum correlations in mixed states. The states studied are modelled by a two-qubit system interacting with its environment via a quantum nondemolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed and the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation are reported. In addition, a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, is made on these states, generated by the above evolutions. Interestingly, examples are found, of states, where entanglement is vanishing, but discord is non-vanishing, bringing out the fact that entanglement is a subset of quantum correlations.
On the quantum information processing in nuclear magnetic resonance quantum computing experiments
Energy Technology Data Exchange (ETDEWEB)
Azevedo, E.R. de; Bonk, F.A.; Vidoto, E.L.G.; Bonagamba, T.J. [Universidade de Sao Paulo (IFSC/USP), Sao Carlos, SP (Brazil). Inst. de Fisica; Sarthour, R.S.; Guimaraes, A.P.; Oliveira, I.S. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freitas, J.C.C. [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil). Dept. de Fisica
2003-07-01
Full text: Nuclear Magnetic Resonance appeared in the late nineties to be the most promising candidate to run quantum computing algorithms. An impressive number of experiments demonstrating the implementation of all logic gates and quantum algorithms in systems with a small number of qubits stimulated the general excitement about the technique, and greatly promoted the field. Particularly important were those experiments where entanglement of particles were aimed at. Entanglement is the most fundamental (and weird !) aspect of quantum systems, and is at the basis of quantum teleportation and quantum cryptography, yet impossible to prove in NMR experiments. The hardcore of NMR quantum computing are the so-called pseudo-pure states, upon which radiofrequency (RF) pulses act to implement quantum mechanical unitary transformations, promoting changes in both, Zeeman level populations and coherences in the density matrix. Whereas pseudo-pure states are special non-equilibrium diagonal states, coherences encode information about superposition states. Now, one could safely say that the whole business of quantum computing goes about controlling relative ket phases. In spite of the impossibility to univocally associating a given quantum state to a NMR spectrum, it is possible to demonstrate the phase action of RF pulses over relative ket phases, even if no population changes take place. In this talk these issues will be addressed, and we will show experimental results of our own where this is done in the two-qubit quadrupole nuclei {sup 23}Na in C{sub 10}H{sub 21}NaO{sub 4}S liquid crystal. We demonstrate the reversibility of the Hadamard gate, and of a quantum circuit which generates pseudo-Bell states. The success of the operation reaches almost 100% in the case of the state |01+|10, 80% in the cases of |00> + |01> and |10> + |11>, and 65% for the cat-state |00> + |11>. (author)
Classical and quantum phases of low-dimensional dipolar systems
Energy Technology Data Exchange (ETDEWEB)
Cartarius, Florian
2016-09-22
In this thesis we present a detailed study of the phase diagram of ultracold bosonic atoms confined along a tight atomic wave guide, along which they experience an optical lattice potential. In this quasi-one dimensional model we analyse the interplay between interactions and quantum fluctuations in (i) determining the non-equilibrium steady state after a quench and (ii) giving rise to novel equilibrium phases, when the interactions combine the s-wave contact interaction and the anisotropic long range dipole-dipole interactions. In detail, in the first part of the thesis we study the depinning of a gas of impenetrable bosons following the sudden switch of of the optical lattice. By means of a Bose-Fermi mapping we infer the exact quantum dynamical evolution and show that in the thermodynamic limit the system is in a non-equilibrium steady state without quasi-long range order. In the second part of the thesis, we study the effect of quantum fluctuations on the linear-zigzag instability in the ground state of ultracold dipolar bosons, as a function of the strength of the transverse confinement. We first analyse the linear-zigzag instability in the classical regime, and then use our results to develop a multi-mode Bose-Hubbard model for the system. We then develop several numerical methods, to determine the ground state.
Exciton-driven quantum phase transitions in holography
Gubankova, E; Schalm, K; Zaanen, J
2014-01-01
We study phase transitions driven by fermionic double-trace deformations in gauge-gravity duality. Both the strength of the double trace deformation and the infrared conformal dimension/self-energy scaling of the quasiparticle can be used to decrease the critical temperature to zero, leading to a line of quantum critical points. The self-energy scaling is controlled indirectly through an applied magnetic field and the quantum phase transition naturally involves the condensation of a fermion bilinear which models the spin density wave in antiferromagnetic state. The nature of the quantum critical points depends on the parameters and we find either a BKT-type transition or one of two distinct second order transitions with non-mean field exponents. One of these is an anomalous branch where the order parameter of constituent non-Fermi liquid quasiparticles is enhanced by the magnetic field. Stabilization of ordered non-Fermi liquids by a strong magnetic field is observed in experiments with highly oriented pyroli...
Phase-controlled coherent population trapping in superconducting quantum circuits
Institute of Scientific and Technical Information of China (English)
程广玲; 王一平; 陈爱喜
2015-01-01
We investigate the influences of the-applied-field phases and amplitudes on the coherent population trapping behavior in superconducting quantum circuits. Based on the interactions of the microwave fields with a single∆-type three-level fluxonium qubit, the coherent population trapping could be obtainable and it is very sensitive to the relative phase and amplitudes of the applied fields. When the relative phase is tuned to 0 orπ, the maximal atomic coherence is present and coherent population trapping occurs. While for the choice ofπ/2, the atomic coherence becomes weak. Meanwhile, for the fixed relative phaseπ/2, the value of coherence would decrease with the increase of Rabi frequency of the external field coupled with two lower levels. The responsible physical mechanism is quantum interference induced by the control fields, which is indicated in the dressed-state representation. The microwave coherent phenomenon is present in our scheme, which will have potential applications in optical communication and nonlinear optics in solid-state devices.
Cavity quantum networks for quantum information processing in decoherence-free subspace
Institute of Scientific and Technical Information of China (English)
Hua WEI; Zhi-jiao DENG; Wan-li YANG; Fei ZHOU
2009-01-01
We give a brief review on the quantum infor- mation processing in decoherence-free subspace (DFS). We show how to realize the initialization of the entangled quantum states, information transfer and teleportation of quantum states, two-qubit Grover search and how to construct the quantum network in DFS, within the cav- ity QED regime based on a cavity-assisted interaction by single-photon pulses.
Schroeder, Almut; Ubaid-Kassis, Sara; Vojta, Thomas
2011-03-09
We report magnetization measurements close to the ferromagnetic quantum phase transition of the d-metal alloy Ni(1 - x)V(x) at a vanadium concentration of x(c)≈11.4%. In the diluted regime (x > x(c)), the temperature (T) and magnetic field (H) dependences of the magnetization are characterized by nonuniversal power laws and display H/T scaling in a wide temperature and field range. The exponents vary strongly with x and follow the predictions of a quantum Griffiths phase. We also discuss the deviations and limits of the quantum Griffiths phase as well as the phase boundaries due to bulk and cluster physics.
Stability of Mixed Nash Equilibria in Symmetric Quantum Games
Institute of Scientific and Technical Information of China (English)
A.Iqbal; A.H.Toor
2004-01-01
In bimatrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium.
Characterization of Quantum Phase Transition using Holographic Entanglement Entropy
Ling, Yi; Wu, Jian-Pin
2016-01-01
We investigate the holographic entanglement entropy (HEE) in Einstein-Maxwell-Dilaton theory. In this framework black brane solutions with vanishing entropy density in zero temperature limit have been constructed in the presence of Q-lattice structure. We find that the first order derivative of HEE with repsect to lattice parameters exhibits the maximization behavior near quantum critical points (QCPs), which coincides with the phenomenon observed in realistic condensed matter system. Our discovery in this letter extends our previous observation in arXiv:1502.03661 where HEE itself diagnoses the quantum phase transition (QPT) with local extremes. We propose that it would be a univeral feature that HEE or its derivatives with respect to system parameters can characterize QPT in a generic holographic system.
Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang-Baxter system
Hu, Taotao; Yang, Qi; Xue, Kang; Wang, Gangcheng; Zhang, Yan; Li, Xiaodan; Ren, Hang
2017-01-01
In this paper, we investigate the ground-state fidelity and fidelity susceptibility in the many-body Yang-Baxter system and analyze their connections with quantum phase transition. The Yang-Baxter system was perturbed by a twist of e^{iφ} at each bond, where the parameter φ originates from the q-deformation of the braiding operator U with q = e^{-iφ} (Jimbo in Yang-Baxter equations in integrable systems, World Scientific, Singapore, 1990), and φ has a physical significance of magnetic flux (Badurek et al. in Phys. Rev. D 14:1177, 1976). We test the ground-state fidelity related by a small parameter variation φ which is a different term from the one used for driving the system toward a quantum phase transition. It shows that ground-state fidelity develops a sharp drop at the transition. The drop gets sharper as system size N increases. It has been verified that a sufficiently small value of φ used has no effect on the location of the critical point, but affects the value of F(gc,φ) . The smaller the twist φ, the more the value of F(gc,φ) is close to 0. In order to avoid the effect of the finite value of φ, we also calculate the fidelity susceptibility. Our results demonstrate that in the Yang-Baxter system, the quantum phase transition can be well characterized by the ground-state fidelity and fidelity susceptibility in a special way.
Learning algorithm and application of quantum BP neural networks based on universal quantum gates
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A quantum BP neural networks model with learning algorithm is proposed.First,based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate,a quantum neuron model is constructed,which is composed of input,phase rotation,aggregation,reversal rotation and output.In this model,the input is described by qubits,and the output is given by the probability of the state in which |1＞ is observed.The phase rotation and the reversal rotation are performed by the universal quantum gates.Secondly,the quantum BP neural networks model is constructed,in which the output layer and the hide layer are quantum neurons.With the application of the gradient descent algorithm,a learning algorithm of the model is proposed,and the continuity of the model is proved.It is shown that this model and algorithm are superior to the conventional BP networks in three aspects: convergence speed,convergence rate and robustness,by two application examples of pattern recognition and function approximation.
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
Arvind
2001-02-01
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically
Quarks and gluons in the phase diagram of quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Welzbacher, Christian Andreas
2016-07-14
In this dissertation we study the phase diagram of strongly interacting matter by approaching the theory of quantum chromodynamics in the functional approach of Dyson-Schwinger equations. With these quantum (field) equations of motions we calculate the non-perturbative quark propagator within the Matsubara formalism. We built up on previous works and extend the so-called truncation scheme, which is necessary to render the infinite tower of Dyson-Schwinger equations finite and study phase transitions of chiral symmetry and the confinement/deconfinement transition. In the first part of this thesis we discuss general aspects of quantum chromodynamics and introduce the Dyson-Schwinger equations in general and present the quark Dyson-Schwinger equation together with its counterpart for the gluon. The Bethe-Salpeter equation is introduced which is necessary to perform two-body bound state calculations. A view on the phase diagram of quantum chromodynamics is given, including the discussion of order parameter for chiral symmetry and confinement. Here we also discuss the dependence of the phase structure on the masses of the quarks. In the following we present the truncation and our results for an unquenched N{sub f} = 2+1 calculation and compare it to previous studies. We highlight some complementary details for the quark and gluon propagator and discus the resulting phase diagram, which is in agreement with previous work. Results for an equivalent of the Columbia plot and the critical surface are discussed. A systematically improved truncation, where the charm quark as a dynamical quark flavour is added, will be presented in Ch. 4. An important aspect in this investigation is the proper adjustment of the scales. This is done by matching vacuum properties of the relevant pseudoscalar mesons separately for N{sub f} = 2+1 and N f = 2+1+1 via a solution of the Bethe-Salpeter equation. A comparison of the resulting N{sub f} = 2+1 and N{sub f} = 2+1+1 phase diagram indicates
Experiments on Quantum Hall Topological Phases in Ultra Low Temperatures
Energy Technology Data Exchange (ETDEWEB)
Du, Rui-Rui [Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
2015-02-14
This project is to cool electrons in semiconductors to extremely low temperatures and to study new states of matter formed by low-dimensional electrons (or holes). At such low temperatures (and with an intense magnetic field), electronic behavior differs completely from ordinary ones observed at room temperatures or regular low temperature. Studies of electrons at such low temperatures would open the door for fundamental discoveries in condensed matter physics. Present studies have been focus on topological phases in the fractional quantum Hall effect in GaAs/AlGaAs semiconductor heterostructures, and the newly discovered (by this group) quantum spin Hall effect in InAs/GaSb materials. This project consists of the following components: 1) Development of efficient sample cooling techniques and electron thermometry: Our goal is to reach 1 mK electron temperature and reasonable determination of electron temperature; 2) Experiments at ultra-low temperatures: Our goal is to understand the energy scale of competing quantum phases, by measuring the temperature-dependence of transport features. Focus will be placed on such issues as the energy gap of the 5/2 state, and those of 12/5 (and possible 13/5); resistive signature of instability near 1/2 at ultra-low temperatures; 3) Measurement of the 5/2 gaps in the limit of small or large Zeeman energies: Our goal is to gain physics insight of 5/2 state at limiting experimental parameters, especially those properties concerning the spin polarization; 4) Experiments on tuning the electron-electron interaction in a screened quantum Hall system: Our goal is to gain understanding of the formation of paired fractional quantum Hall state as the interaction pseudo-potential is being modified by a nearby screening electron layer; 5) Experiments on the quantized helical edge states under a strong magnetic field and ultralow temperatures: our goal is to investigate both the bulk and edge states in a quantum spin Hall insulator under time
Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
Bittencourt, Victor A. S. V.; Bernardini, Alex E.; Blasone, Massimo
2016-05-01
Quantum transition probabilities and quantum entanglement for two-qubit states of a four-level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a SU(2 )⊗SU(2 ) group structure. Using the correspondence of the method of simulating a 3 +1 dimensional Dirac-like Hamiltonian for bispinor particles into a single trapped ion, one preliminarily obtains the analytical tools for describing ionic state transition probabilities as a typical quantum oscillation feature. For Dirac-like structures driven by generalized Poincaré classes of coupling potentials, one also identifies the SU(2 )⊗SU(2 ) internal degrees of freedom corresponding to intrinsic parity and spin polarization as an adaptive platform for computing the quantum entanglement between the internal quantum subsystems which define two-qubit ionic states. The obtained quantum correlational content is then translated into the quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the trapping magnetic field. Experimentally, the controllable parameters simulated by ion traps can be mapped into a Dirac-like system in the presence of an electrostatic field which, in this case, is associated to ionic carrier interactions. Besides exhibiting a complete analytical profile for ionic quantum transitions and quantum entanglement, our results indicate that carrier interactions actively drive an overall suppression of the quantum entanglement.
Wang, Hao-Tian; Zou, Yang; Ge, Rong-Chun; Guo, Guang-Can
2010-01-01
We present a detailed study of the entanglement dynamics of a two-qubit system coupled to independent non-Markovian environments, employing hierarchy equations. This recently developed theoretical treatment can conveniently solve non-Markovian problems and take into consideration the correlation between the system and bath in an initial state. We concentrate on calculating the death and rebirth time points of the entanglement to obtain a general view of the concurrence curve and explore the behavior of entanglement dynamics with respect to the coupling strength, the characteristic frequency of the noise bath and the environment temperature.
Implementing phase-covariant cloning in circuit quantum electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Zhu, Meng-Zheng [School of Physics and Material Science, Anhui University, Hefei 230039 (China); School of Physics and Electronic Information, Huaibei Normal University, Huaibei 235000 (China); Ye, Liu, E-mail: yeliu@ahu.edu.cn [School of Physics and Material Science, Anhui University, Hefei 230039 (China)
2016-10-15
An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.
Implementing phase-covariant cloning in circuit quantum electrodynamics
Zhu, Meng-Zheng; Ye, Liu
2016-10-01
An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.
Quantum mechanical force fields for condensed phase molecular simulations
Giese, Timothy J.; York, Darrin M.
2017-09-01
Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.
Unconventional transformation of spin Dirac phase across a topological quantum phase transition.
Xu, Su-Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J Hugo; Shibayev, Pavel P; Basak, Susmita; Chang, Tay-Rong; Jeng, Horng-Tay; Cava, Robert J; Lin, Hsin; Bansil, Arun; Hasan, M Zahid
2015-04-17
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.
Dimensionless ratios: Characteristics of quantum liquids and their phase transitions
Yu, Yi-Cong; Chen, Yang-Yang; Lin, Hai-Qing; Römer, Rudolf A.; Guan, Xi-Wen
2016-11-01
Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio, and the Wiedemann-Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multicomponent quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility, and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multiresistor networks in series and parallel—a novel and useful characteristic of multicomponent Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realized multispecies cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.
Fast gain and phase recovery of semiconductor optical amplifiers based on submonolayer quantum dots
Energy Technology Data Exchange (ETDEWEB)
Herzog, Bastian, E-mail: BHerzog@physik.tu-berlin.de; Owschimikow, Nina; Kaptan, Yücel; Kolarczik, Mirco; Switaiski, Thomas; Woggon, Ulrike [Institut für Optik und Atomare Physik, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin (Germany); Schulze, Jan-Hindrik; Rosales, Ricardo; Strittmatter, André; Bimberg, Dieter; Pohl, Udo W. [Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin (Germany)
2015-11-16
Submonolayer quantum dots as active medium in opto-electronic devices promise to combine the high density of states of quantum wells with the fast recovery dynamics of self-assembled quantum dots. We investigate the gain and phase recovery dynamics of a semiconductor optical amplifier based on InAs submonolayer quantum dots in the regime of linear operation by one- and two-color heterodyne pump-probe spectroscopy. We find an as fast recovery dynamics as for quantum dot-in-a-well structures, reaching 2 ps at moderate injection currents. The effective quantum well embedding the submonolayer quantum dots acts as a fast and efficient carrier reservoir.
Security of practical phase-coding quantum key distribution
Li, Hong-Wei; Han, Zheng-Fu; Bao, Wan-Su; Guo, Guang-Can
2009-01-01
Security proof of practical quantum key distribution (QKD) has attracted a lot of attentions in recent years. Most of real-life QKD implementations are based on phase-coding BB84 protocol, which usually uses Unbalanced Mach-Zehnder Interferometer (UMZI) as the information coder and decoder. However, the long arm and short arm of UMZI will introduce different loss in practical experimental realizations, the state emitted by Alice's side is nolonger standard BB84 states. In this paper, we will give a security analysis in this situation. Counterintuitively, active compensation for this different loss will only lower the secret key bit rate.
Quantum Phase Transition in the Shape of Zr isotopes
Togashi, Tomoaki; Otsuka, Takaharu; Shimizu, Noritaka
2016-01-01
The rapid shape change in Zr isotopes near neutron number $N$=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its $0g_{9/2}$ orbit, and is shown to be a quantum phase transition. Monte Carlo shell-model calculations are carried out for Zr isotopes of $N$=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in a good agreement with experiments, depicting various shapes in going from $N$=50 to 70. Novel coexistence of prolate and triaxial shapes is suggested.
Phase space view of quantum mechanical systems and Fisher information
Nagy, Á.
2016-06-01
Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Quantum dynamics via a time propagator in Wigner's phase space
DEFF Research Database (Denmark)
Grønager, Michael; Henriksen, Niels Engholm
1995-01-01
that the simple classical deterministic motion breaks down surprisingly fast in an anharmonic potential. Finally, we discuss the possibility of using the scheme as a useful approach to quantum dynamics in many dimensions. To that end we present a Monte Carlo integration scheme using the norm of the propagator......We derive an expression for a short-time phase space propagator. We use it in a new propagation scheme and demonstrate that it works for a Morse potential. The propagation scheme is used to propagate classical distributions which do not obey the Heisenberg uncertainty principle. It is shown...
The Phase Space Formulation of Time-Symmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Charlyne de Gosson
2015-11-01
Full Text Available Time-symmetric quantum mechanics can be described in the Weyl–Wigner–Moyal phase space formalism by using the properties of the cross-terms appearing in the Wigner distribution of a sum of states. These properties show the appearance of a strongly oscillating interference between the pre-selected and post-selected states. It is interesting to note that the knowledge of this interference term is sufficient to reconstruct both states.Quanta 2015; 4: 27–34.
Quantum key distribution based on phase encoding and polarization measurement
Ma, H Q; Zhao, J L; Ma, Hai-Qiang; Wu, Ling-An; Zhao, Jian-Ling
2007-01-01
A one-way quantum key distribution scheme based on intrinsically stable Faraday-mirror type Michelson interferometers with four-port polarizing beampslitters has been demonstrated which can compensate for birefringence effects automatically. The encoding is performed with phase modulators, but decoding is accomplished through measurement of the polarization state of Bob's photons. An extinction ratio of about 30dB was maintained for several hours over 50km of fiber at 1310nm without any adjustment to the setup, which shows its good potential for practical systems
Quantum phase transitions about parity breaking in matrix product systems
Institute of Scientific and Technical Information of China (English)
ZHU Jing-Min
2011-01-01
According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.
Generation of entanglement in quantum parametric oscillators using phase control.
Gonzalez-Henao, J C; Pugliese, E; Euzzor, S; Abdalah, S F; Meucci, R; Roversi, J A
2015-08-19
The control of quantum entanglement in systems in contact with environment plays an important role in information processing, cryptography and quantum computing. However, interactions with the environment, even when very weak, entail decoherence in the system with consequent loss of entanglement. Here we consider a system of two coupled oscillators in contact with a common heat bath and with a time dependent oscillation frequency. The possibility to control the entanglement of the oscillators by means of an external sinusoidal perturbation applied to the oscillation frequency has been theoretically explored. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart is unstable, otherwise when the classical system is stable, entanglement is not possible. Therefore, we can control the entanglement swapping from stable to unstable regions by adjusting amplitude and phase of our external controller. We also show that the entanglement rate is approximately proportional to the real part of the Floquet coefficient of the classical counterpart of the oscillators. Our results have the intriguing peculiarity of manipulating quantum information operating on a classical system.
Novel quantum behavior generated by traveling across a quantum phase transition
Acevedo, O. L.; Rodriguez, F. J.; Quiroga, L.; Johnson, N. F.
2012-02-01
We report novel dynamical behavior in a multi-qubit--light system described by the Dicke model, which is being driven across its thermodynamic quantum-phase boundary. Analyzing the system's quantum fidelity, we find that the near-adiabatic regime exhibits the richest phenomena, with a strong asymmetry in the internal collective dynamics depending on which phase is the starting point. Depending on the quenching regime a highly non-trivial behavior emerges in both the qubit and radiation subsystems. For the former, we find that for some paths in parameter space the final fidelity of the near-adiabatic process does not depend on the direction of the trajectory, but depends only on the speed at which the path is traveled. This behavior is contrasted with Landau-Zener tunneling and the Kibble-Zurek mechanism. Furthermore, for some qubit subsystems, we identify purification and screening effects which could be used for quantum control. By contrast, the evolution of the Wigner function shows the radiation subsystem exhibits the emergence of complexity and non-classicality. These findings could be experimentally tested in several condensed matter scenarios -- for example, diamond-NV centers and superconductor qubits in confined radiation environments.
Controlled quantum state transfer via parity measurement
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this work,a scheme for controlled quantum state transfer is proposed using parity measurement in a cavity-waveguide system.As two special cases,two schemes of controlled quantum state transfer for one qubit and two qubits are investigated in detail.An important advantage is that controlled quantum state transfer can be completed by single-qubit rotations and the measurement of parity.Therefore,the present scheme might be realized in the scope of current experimental technology.
Controlled quantum state transfer via parity measurement
Institute of Scientific and Technical Information of China (English)
YUAN Quan; LI JiuHui
2009-01-01
In this work, a scheme for controlled quantum state transfer is proposed using parity measurement in a cavity-waveguide system. As two special cases, two schemes of controlled quantum state transfer for one qubit and two qubits are investigated in detail. An important advantage is that controlled quantum state transfer can be completed by single-qubit rotations and the measurement of parity. Therefore, the present scheme might be realized in the scope of current experimental technology.
Hua, Ming; Tao, Ming-Jie; Deng, Fu-Guo
2016-02-24
We propose a quantum processor for the scalable quantum computation on microwave photons in distant one-dimensional superconducting resonators. It is composed of a common resonator R acting as a quantum bus and some distant resonators rj coupled to the bus in different positions assisted by superconducting quantum interferometer devices (SQUID), different from previous processors. R is coupled to one transmon qutrit, and the coupling strengths between rj and R can be fully tuned by the external flux through the SQUID. To show the processor can be used to achieve universal quantum computation effectively, we present a scheme to complete the high-fidelity quantum state transfer between two distant microwave-photon resonators and another one for the high-fidelity controlled-phase gate on them. By using the technique for catching and releasing the microwave photons from resonators, our processor may play an important role in quantum communication as well.
Quantum spin Hall phase in 2D trigonal lattice
Wang, Z. F.; Jin, Kyung-Hwan; Liu, Feng
2016-09-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin-orbit coupling (SOC)-induced s-p band inversion or p-p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ~73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types.
Bastos, Catarina; Santos, Jonas F G
2014-01-01
Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of the Zeeman effect, the momentum space NC parameter introduces mutual information properties quantified by the linear entropy related to the relevant Hilbert space coordinates. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.
Phase-controlled superconducting heat-flux quantum modulator
Giazotto, F.; Martínez-Pérez, M. J.
2012-09-01
We theoretically put forward the concept of a phase-controlled superconducting heat-flux quantum modulator. Its operation relies on phase-dependent heat current predicted to occur in temperature-biased Josephson tunnel junctions. The device behavior is investigated as a function of temperature bias across the junctions, bath temperature, and junctions asymmetry as well. In a realistic Al-based setup the structure could provide temperature modulation amplitudes up to ˜50 mK with flux-to-temperature transfer coefficients exceeding ˜125 mK/Φ0 below 1 K, and temperature modulation frequency of the order of a few MHz. The proposed structure appears as a promising building-block for the implementation of caloritronic devices operating at cryogenic temperatures.
Coherent quantum squeezing due to the phase space noncommutativity
Bernardini, Alex E
2015-01-01
The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard billiards is obtained and their components behavior are monitored in time. It is assumed that the independent degrees of freedom are two \\emph{free} 1D harmonic oscillators (HO's), so the system Hamiltonian does not contain interaction terms. Through the noncommutative deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained Hamiltonian represents then two \\emph{interacting} 1D HO's. By assuming that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed...
Quantum phases of a chain of strongly interacting anyons
Finch, Peter E.; Frahm, Holger; Lewerenz, Marius; Milsted, Ashley; Osborne, Tobias J.
2014-08-01
Quantum gates for the manipulation of topological qubits rely on interactions between non-Abelian anyonic quasiparticles. We study the collective behavior of systems of anyons arising from such interactions. In particular, we study the effect of favoring different fusion channels of the screened Majorana spins appearing in the recently proposed topological Kondo effect. Based on the numerical solution of a chain of SO(5)2 anyons we identify two critical phases whose low-energy behavior is characterized by conformal field theories with central charges c =1 and c =8/7, respectively. Our results are complemented by exact results for special values of the coupling constants which provide additional information about the corresponding phase transitions.
Polarons and Mobile Impurities Near a Quantum Phase Transition
Shadkhoo, Shahriar
This dissertation aims at improving the current understanding of the physics of mobile impurities in highly correlated liquid-like phases of matter. Impurity problems pose challenging and intricate questions in different realms of many-body physics. For instance, the problem of ''solvation'' of charged solutes in polar solvents, has been the subject of longstanding debates among chemical physicists. The significant role of quantum fluctuations of the solvent, as well as the break down of linear response theory, render the ordinary treatments intractable. Inspired by this complicated problem, we first attempt to understand the role of non-specific quantum fluctuations in the solvation process. To this end, we calculate the dynamic structure factor of a model polar liquid, using the classical Molecular Dynamics (MD) simulations. We verify the failure of linear response approximation in the vicinity of a hydrated electron, by comparing the outcomes of MD simulations with the predictions of linear response theory. This nonlinear behavior is associated with the pronounced peaks of the structure factor, which reflect the strong fluctuations of the local modes. A cavity picture is constructed based on heuristic arguments, which suggests that the electron, along with the surrounding polarization cloud, behave like a frozen sphere, for which the linear response theory is broken inside and valid outside. The inverse radius of the spherical region serves as a UV momentum cutoff for the linear response approximation to be applicable. The problem of mobile impurities in polar liquids can be also addressed in the framework of the ''polaron'' problem. Polaron is a quasiparticle that typically acquires an extended state at weak couplings, and crossovers to a self-trapped state at strong couplings. Using the analytical fits to the numerically obtained charge-charge structure factor, a phenomenological approach is proposed within the Leggett's influence functional formalism, which
Phase Interference in a Multi-level Quantum-Dot System
Institute of Scientific and Technical Information of China (English)
ZHANG Xu-Ming; CHEN Xiao-Shuang; LU Wei
2009-01-01
@@ Considering phase interference, we investigate coherent transport in a quantum dot by using a thermopower. In the single process of the electronic transport through the quantum dot, it is shown that the phase interference between the levels of a quantum dot is like the Aharonov-Bohm effect. The result indicates that the thermopower is very sensitive to phase interference. It is also found that the phase-difference change of the different levels of the quantum dot can determine the shape of the thermopower.
Enhanced Cross-Phase Modulation via Phase Control in a Quantum dot Nanostructure
Institute of Scientific and Technical Information of China (English)
郝向英; 郑安寿; 王英; 李小刚
2012-01-01
A four-level quantum dot （QD） nanostructure interacting with four fields （two weak near-infrared （NIR） pulses and two control fields） forms the well-known double-cascade configuration.We investigate the cross-phase modulation （XPM） between the two NIR pulses.The results show,in such a closed-loop scheme,that the XPM can be greatly enhanced,while the linear absorption and two-photon absorption （gain） can be efficiently depressed by tuning the relative phase among the applied fields.This protocol may have potential applications in NIR all-optical switch design and quantum information processing with the solid-state materials.
Quantum Computer Using Coupled Quantum Dot Molecules
Wu, N J; Natori, A; Yasunaga, H; Wu*, Nan-Jian
1999-01-01
We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can...
Demonstration of a quantum logic gate in a cryogenic surface-electrode ion trap
Wang, Shannon X; Ge, Yufei; Shewmon, Ruth; Chuang, Isaac L
2009-01-01
We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. AC Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminating the need for an additional laser. Quantum process tomography is implemented on atomic and motional states using conditional pulse sequences. With these techniques we demonstrate a Cirac-Zoller Controlled-NOT gate in a single ion with a mean fidelity of 91(1)%.
Quantum logic gates with two-level trapped ions beyond Lamb-Dicke limit
Institute of Scientific and Technical Information of China (English)
Zheng Xiao-Juan; Luo Yi-Min; Cai Jian-Wu
2009-01-01
In the system with two two-level ions confined in a linear trap,this paper presents a simple scheme to realize the quantum phase gate(QPG)and the swap gate beyond the Lamb-Dicke(LD)limit.These two-qubit quantum logic gates only involve the internal states of two trapped ions.The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers.Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme.Thus the scheme is simple and the interaction time is very short,which is important in view of decoherence.The experimental feasibility for achieving this scheme is also discussed.
Lari, Behzad
2011-01-01
This is a thesis submitted to university of Pune, India, for the Ph.D. degree. This work deals with entanglement production in two qubit, two qutrit and three qubit systems, entanglement in indistinguishable fermionic systems, quantum discord in a Heisenberg chain and geometric measure of quantum discord in an arbitrary state of a bipartite quantum system.
Nagy, D.; Domokos, P.
2015-07-01
We show that the critical exponent of a quantum phase transition in a damped-driven open system is determined by the spectral density function of the reservoir. We consider the open-system variant of the Dicke model, where the driven boson mode and also the large N spin couple to independent reservoirs at zero temperature. The critical exponent, which is 1 if there is no spin-bath coupling, decreases below 1 when the spin couples to a sub-Ohmic reservoir.
Experimental estimation of entanglement at the quantum limit.
Brida, Giorgio; Degiovanni, Ivo Pietro; Florio, Angela; Genovese, Marco; Giorda, Paolo; Meda, Alice; Paris, Matteo G A; Shurupov, Alexander
2010-03-12
Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.
Fu, Jian
2010-01-01
We demonstrate that a tensor product structure could be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using classical fields modulated with pseudorandom phase sequences, we discuss efficient simulation of several typical quantum states, including product state, Bell states, GHZ state, and W state. By performing quadrature demodulation scheme, we could obtain the mode status matrix of the simulating classical fields, based on which we propose a sequence permutation mechanism to reconstruct the simulated quantum states. The research on classical simulation of quantum states is important, for it not only enables potential practical applications in quantum computation, but also provides useful insights into fundamental concepts of quantum mechanics.
Fu, Jian; Xu, Yingying; Dong, Hongtao
2010-01-01
We demonstrate that n classical fields modulated with n different pseudorandom phase sequences can constitute a 2^n-dimensional Hilbert space that contains tensor product structure. By using classical fields modulated with pseudorandom phase sequences, we discuss effective simulation of Bell states and GHZ state, and apply both correlation analysis and von Neumann entropy to characterize the simulation. We obtain similar results with the cases in quantum mechanics and find that the conclusions can be easily generalized to n quantum particles. The research on simulation of quantum entanglement may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation.
Quantum spin/valley Hall effect and topological insulator phase transitions in silicene
Tahir, M.
2013-04-26
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments.
Beyond the Dirac phase factor: Dynamical Quantum Phase-Nonlocalities in the Schroedinger Picture
Moulopoulos, Konstantinos
2011-01-01
Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of wavefunctions in the Schroedinger Picture. These nonlocal phase behaviors, apparently overlooked in path-integral approaches, give a natural account of the dynamical nonlocality character of the various (even static) Aharonov-Bohm phenomena, while at the same time they seem to respect Causality. Indeed, for particles passing through nonvanishing magnetic or electric fields they lead to cancellations of Aharonov-Bohm phases at the observation point, generalizing earlier semiclassical experimental observations (of Werner & Brill) to delocalized (spread-out) quantum states. This leads to a correction of previously unnoticed sign-errors in the literature, and to a natural explanation of the deeper reason why certa...
A magnetically induced quantum phase transition in holography
Gnecchi, A; Papadoulaki, O; Toldo, C
2016-01-01
We investigate quantum phase transitions in a 2+1 dimensional gauge theory at finite chemical potential $\\chi$ and magnetic field $B$. The gravity dual is based on 4D $\\mathcal{N}=2$ Fayet-Iliopoulos gauged supergravity and the solutions we consider---that are constructed analytically---are extremal, dyonic, asymptotically $AdS_4$ black-branes with a nontrivial radial profile for the scalar field. We discover a line of second order fixed points at $B=B_c(\\chi)$ between the dyonic black brane and an extremal "thermal gas" solution with a singularity of good-type, according to the acceptability criteria of Gubser [1]. The dual field theory is the ABJM theory [2] deformed by a triple trace operator $\\Phi^3$ and placed at finite charge and magnetic field. This line of fixed points might be useful in studying the various strongly interacting quantum critical phenomena such as the ones proposed to underlie the cuprate superconductors. We also find curious similarities between the behaviour of the VeV $\\langle \\Phi ...
Continuous-time cross-phase modulation and quantum computation
Shapiro, J H; Razavi, Mohsen; Shapiro, Jeffrey H.
2006-01-01
The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyze the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will degrade the performance of the parity gate proposed by Munro, Nemoto, and Spiller [New J. Phys. 7, 137 (2005)].
Liu, Bao; Zhang, Feng-Yang; Song, Jie; Song, He-Shan
2015-01-01
We propose a direct measurement scheme to read out the geometric phase of a coupled double quantum dot system via a quantum point contact(QPC) device. An effective expression of the geometric phase has been derived, which relates the geometric phase of the double quantum dot qubit to the current through QPC device. All the parameters in our expression are measurable or tunable in experiment. Moreover, since the measurement process affects the state of the qubit slightly, the geometric phase can be protected. The feasibility of the scheme has been analyzed. Further, as an example, we simulate the geometrical phase of a qubit when the QPC device is replaced by a single electron transistor(SET). PMID:26121538
Phase sensitive quantum interference on forbidden transition in ladder scheme
Koganov, Gennady A
2014-01-01
A three level ladder system is analyzed and the coherence of initially electric-dipole forbidden transition is calculated. Due to the presence of two laser fields the initially dipole forbidden transition becomes dynamically permitted due to ac Stark effect. It is shown that such transitions exhibit quantum-interference-related phenomena, such as electromagnetically induced transparency, gain without inversion and enhanced refractive index. Gain and dispersion characteristics of such transitions strongly depend upon the relative phase between the driving and the probe fields. Unlike allowed transitions, gain/absorption behavior of ac-Stark allowed transitions exhibit antisymmetric feature on the Rabi sidebands. It is found that absorption/gain spectra possess extremely narrow sub-natural resonances on these ac Stark allowed forbidden transitions. An interesting finding is simultaneous existence of gain and negative dispersion at Autler-Townes transition which may lead to both reduction of the group velocity a...
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
DIÓGENES CAMPOS
2017-03-01
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
Quantum Phase Transitions of Hard-Core Bosons on the Kagome Lattice
Isakov, S. V.; Melko, R. G.; Sengupta, K.; Wessel, S.; Kim, Yong Baek
2006-03-01
We study hard-core bosons with nearest-neighbor repulsion on the kagome lattice at different filling factors using quantum Monte Carlo simulations and a dual vortex theory. At half-filling, the ground state of the system is always a uniform superfluid in contrast to the case of the triangular lattice. There exists a quantum phase transition from a superfluid to a valence bond solid phase away from half-filling. The possibility of unusual quantum criticality is investigated.
Hybrid quantum processors: molecular ensembles as quantum memory for solid state circuits.
Rabl, P; DeMille, D; Doyle, J M; Lukin, M D; Schoelkopf, R J; Zoller, P
2006-07-21
We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that, for convenient trap-surface distances of a few microm, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.
Hybrid Quantum Processors: molecular ensembles as quantum memory for solid state circuits
Rabl, P; Doyle, J M; Lukin, M D; Schölkopf, R J; Zoller, P
2006-01-01
We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that for convenient trap-surface distances of a few $\\mu$m, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.
Phase dependent spin manipulation in a single quantum dot
Energy Technology Data Exchange (ETDEWEB)
Santana, Ted S.; Villas-Boas, Jose M. [Universidade Federal de Uberlandia (UFU), MG (Brazil). Inst. de Fisica
2012-07-01
Full text: Spin qubits in semiconductor quantum dots (QD) have attracted a lot of attention since the seminal work of Loss and DiVincenzo [1]. Controlling a single electron spin in a QD is a key ingredient for implementing a quantum information device in a solid-state system. Using ultra fast optical control is very attractive due to the possibility to achieve a spin rotation in a picosecond timescale, much shorter than the spin coherence time in such system [2]. In this work we use a density matrix formalism to model the dynamics of a system composed of a single electron loaded in a QD with a magnetic field applied in the Voigt geometry [3] and we show that it is possible to coherent manipulate its spin degree of freedom by applying two lasers pulses with different frequency, polarization and relative phase. For lasers with large detuning we can adiabatically eliminate the trion states (two electrons and one hole in the QD), obtaining an effective Hamiltonian which only couples the two electron spin. The effective coupling is strongly dependent on the relative phase between the pulses, making it possible to complete switch it on and off when desired. For phase {phi} = 0 we see the typical Rabi oscillation, as experimentally observed in Ref. [3], while for phase {phi} = {pi}/2 the interaction is completely switched off. We further investigated the common approximation used in this system which consist of reducing the four-level to a three-level system based on the large laser detuning [3]. Numerical and analytical results show that this approximation can only be used for very large Zeeman split, which cannot be achieved in InAs self-assembled QD with reasonable magnetic fields. The fourth level cannot be neglected here because the two laser pulses create an interference effect (not present in a three level system) between the different transitions and a large laser detuning does not eliminate its influence. [1] Loss D and DiVincenzo D P 1998, Phys. Rev. A 57, 120
Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer.
Gulde, Stephan; Riebe, Mark; Lancaster, Gavin P T; Becher, Christoph; Eschner, Jürgen; Häffner, Hartmut; Schmidt-Kaler, Ferdinand; Chuang, Isaac L; Blatt, Rainer
2003-01-02
Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.
Experimental realization of nonadiabatic holonomic quantum computation.
Feng, Guanru; Xu, Guofu; Long, Guilu
2013-05-10
Because of its geometric nature, holonomic quantum computation is fault tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantum computation in a liquid NMR quantum information processor. Two noncommuting one-qubit holonomic gates, rotations about x and z axes, and the two-qubit holonomic CNOT gate are realized by evolving the work qubits and an ancillary qubit nonadiabatically. The successful realizations of these universal elementary gates in nonadiabatic holonomic quantum computation demonstrates the experimental feasibility of this quantum computing paradigm.
P T phase transition in multidimensional quantum systems
Bender, Carl M.; Weir, David J.
2012-10-01
Non-Hermitian P T-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken P T symmetry in which the eigenvalues are all real, and (ii) a region of broken P T symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the P T phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled P T-symmetric Hamiltonians, H=\\textstyle {\\frac{1}{2}}p^2+\\textstyle {\\frac{1}{2}}x^2+\\textstyle {\\frac{1}{2}}q^2+\\textstyle {\\frac{1}{2}}y^2+igx^2y, H=\\textstyle {\\frac{1}{2}}p^2+\\textstyle {\\frac{1}{2}}x^2+\\textstyle {\\frac{1}{2}}q^2+y^2+igx^2y, H=\\textstyle {\\frac{1}{2}}p^2+\\textstyle {\\frac{1}{2}}x^2+\\textstyle {\\frac{1}{2}}q^2+\\textstyle {\\frac{1}{2}}y^2+\\textstyle {\\frac{1}{2}}r^2+\\textstyle {\\frac{1}{2}}z^2+igxyz, and H=\\textstyle {\\frac{1}{2}}p^2+ \\textstyle {\\frac{1}{2}}x^2+\\textstyle {\\frac{1}{2}}q^2+y^2+\\textstyle {\\frac{1}{2}}r^2+\\textstyle {\\frac{3}{2}}z^2+igxyz are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at g ≈ 0.1, g ≈ 0.04, g ≈ 0.1 and g ≈ 0.05. These results suggest that the P T phase transition is a robust phenomenon not limited to systems having one degree of freedom.
Geometric measure of quantum discord under decoherence
Xiao-Ming, Lu; Sun, Zhe; Wang, Xiaoguang
2010-01-01
The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a 3\\times4 matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement and show that a sudden change in the decay rate of the GMQD does not always imply the sudden change in the decay rate of the quantum discord.
Interqubit coupling mediated by a high-excitation-energy quantum object
Ashhab, S.; Niskanen, A.O.; Harrabi, K.; Nakamura, Y.; Picot, T.; De Groot, P.C.; Harmans, C.J.P.M.; Mooij, J.E.; Nori, F.
2008-01-01
We consider a system composed of two qubits and a high excitation energy quantum object used to mediate coupling between the qubits. We treat the entire system quantum mechanically and analyze the properties of the eigenvalues and eigenstates of the total Hamiltonian. After reproducing well known re
Perfect Biparticle Teleportation by Using Multi-particle Quantum Channel with Joint Measurement
Institute of Scientific and Technical Information of China (English)
GUO Yan-Qing; NIE Jing; REN Zhong-Zhou; LI Chong; CHEN Yu-Qing; YI Xue-Xi
2008-01-01
In this paper, we reinvestigate the faithful quantum teleportation of an arbitrary two-qubit state by a multi-particle channel with multi-particle joint measurements. The relationship between multi-particle quantum channel and the multi-particle joint measurement bases has been found. In addition, we show how to construct the multi-particle joint measurement bases.
Strain-induced topological quantum phase transition in phosphorene oxide
Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun
Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.
Coherent quantum squeezing due to the phase space noncommutativity
Bernardini, Alex E.; Mizrahi, Salomon S.
2015-06-01
The effects of general noncommutativity of operators on producing deformed coherent squeezed states is examined in phase space. A two-dimensional noncommutative (NC) quantum system supported by a deformed mathematical structure, similar to that of Hadamard billiard, is obtained and the components behaviour is monitored in time. It is assumed that the independent degrees of freedom are two free 1D harmonic oscillators (HOs), so the system Hamiltonian does not contain interaction terms. Through the NC deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained, new, Hamiltonian represents two interacting 1D HOs. By admitting that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed in terms of Wigner functions, which are essential to put in evidence the effects of the noncommutativity.
Classical geometric phase of gyro-motion is a coherent quantum Berry phase
Zhu, Hongxuan
2016-01-01
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation is a coherent quantum Berry phase for the coherent states of the Schr\\"odinger equation or the Dirac equation. This equivalence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that orbital Berry phases of the eigenstates interfere coherently such that a coherent Berry phase for the coherent states can be naturally defined, which is exactly the geometric phase of the classical gyro-motion. This technique works for particles with and without spin. For particles with spin, on each of the eigenstates that makes up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the...
Directory of Open Access Journals (Sweden)
T.H. Seligman
2006-02-01
Full Text Available Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits $nsimeq 100-1000$, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strongasymmetry around 90$^circ $ c.m. of evaporating proton yield in the Bi($gamma$,p photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems withexponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization.
Bienert, M.; Flores, J.; Kun, S. Yu.; Seligman, T. H.
2006-02-01
Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits n ≈ 100-1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90° c.m. of evaporating proton yield in the Bi(γ,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).
Bienert, M; Kun, S Yu; Seligman, T H
2006-01-01
Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits $n\\simeq 100$--1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90$^\\circ $ c.m. of evaporating proton yield in the Bi($\\gamma$,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).
Quantum Computation by Pairing Trapped Ultracold Ions
Institute of Scientific and Technical Information of China (English)
冯芒; 朱熙文; 高克林; 施磊
2001-01-01
Superpositional wavefunction oscillations for the implementation of quantum algorithms modify the desired interference required for the quantum computation. We propose a scheme with trapped ultracold ion-pairs beingqubits to diminish the detrimental effect of the wavefunction oscillations, which is applied to the two-qubitGrover's search. It can be also found that the qubits in our scheme are more robust against the decoherencecaused by the environment, and the model is scalable.
Peculiar Quantum Phase Transitions and Hidden Supersymmetry in a Lipkin-Meshkov-Glick Model
Institute of Scientific and Technical Information of China (English)
CHEN Gang; LIANG Jiu-Qing
2009-01-01
In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin-Meshkov-Glick model: an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a first-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another first-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.
Quantum Optical Lattices for Emergent Many-Body Phases of Ultracold Atoms
Caballero-Benitez, Santiago F.; Mekhov, Igor B.
2015-12-01
Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows us to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some phases appear solely due to quantum light-matter correlations. Because of a global, but spatially structured, interaction, the competition between quantum matter and light waves leads to multimode structures even in single-mode cavities, including delocalized dimers of matter-field coherences (bonds), beyond density orders as supersolids and density waves.
Atomic-ensemble-based quantum repeater against general polarization and phase noise
Energy Technology Data Exchange (ETDEWEB)
Zhang Binbin [Department of Electronical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37235 (United States); Xu Yaqiong [Department of Electronical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37235 (United States); Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)
2011-07-15
We present a quantum repeater architecture based on atomic ensembles, which is free of polarization and phase noise. With only simple optical elements, we can obtain the uncorrupted entanglement in the noisy channel. Even if the channel suffers from the general polarization and phase noise, the fidelity of transmitted qubits in our protocol can be stable and have no dependence on the noise parameter, which is a significant advantage compared with previous protocols. Moveover, we can even improve the fidelity by using time delayers. The proposed quantum repeater is feasible and useful in the long-distance quantum entanglement distribution and may be promising in other quantum-information applications.
Microwave spectroscopic observation of distinct electron solid phases in wide quantum wells.
Hatke, A T; Liu, Yang; Magill, B A; Moon, B H; Engel, L W; Shayegan, M; Pfeiffer, L N; West, K W; Baldwin, K W
2014-06-20
In high magnetic fields, two-dimensional electron systems can form a number of phases in which interelectron repulsion plays the central role, since the kinetic energy is frozen out by Landau quantization. These phases include the well-known liquids of the fractional quantum Hall effect, as well as solid phases with broken spatial symmetry and crystalline order. Solids can occur at the low Landau-filling termination of the fractional quantum Hall effect series but also within integer quantum Hall effects. Here we present microwave spectroscopy studies of wide quantum wells that clearly reveal two distinct solid phases, hidden within what in d.c. transport would be the zero diagonal conductivity of an integer quantum-Hall-effect state. Explanation of these solids is not possible with the simple picture of a Wigner solid of ordinary (quasi) electrons or holes.
Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
Ohtsuki, Tomoki; Ohtsuki, Tomi
2016-12-01
Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum Hall and quantum anomalous Hall insulators, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have specific features, but owing to the random nature of systems, determining the matter phase from eigenfunctions is difficult. Here, we propose the deep learning algorithm to capture the features of eigenfunctions. Localization-delocalization transition, as well as disordered Chern insulator-Anderson insulator transition, is discussed.
Phases of quantum states in completely positive non-unitary evolution
De Faria, J G P; Nemes, M C
2003-01-01
We define an operational notion of phases in interferometry for a quantum system undergoing a completely positive non-unitary evolution. This definition is based on the concepts of quantum measurement theory. The suitable generalization of the Pancharatnan connection allows us to determine the dynamical and geometrical parts of the total phase between two states linked by a completely positive map. These results reduce to the knonw expressions of total, dynamical and geometrical phases for pure and mixed states evolving unitarily.
Takeuchi, Shigeki
Quantum information science has been attracting significant attention recently. It harnesses the intrinsic nature of quantum mechanics such as quantum superposition, the uncertainty principle, and quantum entanglement to realize novel functions. Recently, quantum metrology has been emerging as an application of quantum information science. Among the many physical quanta, photons are an indispensable tool for metrology, as light-based measurements are applicable to fields ranging from astronomy to life science. In quantum metrology, quantum entanglement between photons is the phenomenon utilized.In this chapter, we will try to give a brief overview of this emerging field mainly focusing on two topics: Optical phase measurements beyond the standard quantum limit (SQL) and quantum optical coherence tomography (QOCT). The sensitivity of an optical phase measurement for a given photon number N is usually limited by N sqrt{N} , which is called the SQL or shot noise limit. However, the SQL can be overcome when non-classical light is used. We explain the basic concepts and the recent experimental results that exceed the SQL, and an application of this technology for microscopy. QOCT harnesses the quantum entanglement of photons in frequency to cancel out the dispersion effect, which degrades the resolution of conventional OCT. The mechanism of the dispersion cancellation and the latest experimental results will be given.
An Introduction to Quantum Entanglement: a Geometric Approach
Zyczkowski, K; Zyczkowski, Karol; Bengtsson, Ingemar
2006-01-01
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally entangled states. We treat in detail the two-qubit system and emphasise in what respect this case is a special one.
Stability of Mixed Nash Equilibria in Symmetric Quantum Games
Institute of Scientific and Technical Information of China (English)
A. Iqbal; A.H. Toor
2004-01-01
In bimatrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permitpure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initialquantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixedsymmetric Nash equilibrium.
Geometric measure of quantum discord for an arbitrary state of a bipartite quantum system
Hassan, Ali Saif M; Joag, Pramod S
2010-01-01
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. \\textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information. Dakic, Vedral, and Brukner [arXiv:1004.0190 (2010)] introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Luo and Fu [Phys. Rev. A \\textbf{82}, 034302 (2010)] introduced another form for geometric measure of quantum discord. We find an exact formula for the geometric measure of quantum discord for an arbitrary state of a $m\\times n$ bipartite quantum system.
Quantum computation in a quantum-dot-Majorana-fermion hybrid system
Xue, Zheng-Yuan
2012-01-01
We propose a scheme to implement universal quantum computation in a quantum-dot-Majorana-fermion hybrid system. Quantum information is encoded on pairs of Majorana fermions, which live on the the interface between topologically trivial and nontrivial sections of a quantum nanowire deposited on an s-wave superconductor. Universal single-qubit gates on topological qubit can be achieved. A measurement-based two-qubit Controlled-Not gate is produced with the help of parity measurements assisted by the quantum-dot and followed by prescribed single-qubit gates. The parity measurement, on the quantum-dot and a topological qubit, is achieved by the Aharonov- Casher effect.
NMR experimental implementation of three-parties quantum superdense coding
Institute of Scientific and Technical Information of China (English)
WEI Daxiu; YANG Xiaodong; LUO Jun; SUN Xianping; ZENG Xizhi; LIU Maili
2004-01-01
In this study, we report an experiment realization of quantum superdense coding (QSDC) between three parties using nuclear magnetic resonance (NMR). The experimental results have shown that in terms of the QSDC schemes between multiparties proposed by Liu et al. and Crudka et al., three-qubit QSDC can transmit three bits of classical information by sending two qubits only. Our results experimentally show that quantum superdense coding, as one of the quantum information processing protocols, is superior to classical ones.
A Geometric Algebra Perspective On Quantum Computational Gates And Universality In Quantum Computing
Cafaro, Carlo
2010-01-01
We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), we present an explicit algebraic description of one and two-qubit quantum states together with a MSTA characterization of one and two-qubit quantum computational gates. Second, using the above mentioned characterization and the GA description of the Lie algebras SO(3) and SU(2) based on the rotor group Spin+(3, 0) formalism, we reexamine Boykin's proof of universality of quantum gates. We conclude that the MSTA approach does lead to a useful conceptual unification where the complex qubit space and the complex space of unitary operators acting on them become united, with both being made just by multivectors in real space. Finally, the GA approach to rotations based on the rotor group does bring conceptual and computational advantages compared to standard vectoria...
Quantum critical phase and Lifshitz transition in an extended periodic Anderson model.
Laad, M S; Koley, S; Taraphder, A
2012-06-13
We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.
Force law in material media, hidden momentum and quantum phases
Energy Technology Data Exchange (ETDEWEB)
Kholmetskii, Alexander L., E-mail: alkholmetskii@gmail.com [Belarusian State University, Minsk (Belarus); Missevitch, Oleg V. [Institute for Nuclear Problems, Belarusian State University, Minsk (Belarus); Yarman, T. [Okan University, Akfirat, Istanbul (Turkey); Savronik, Eskisehir (Turkey)
2016-06-15
We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.
Confinement-Driven Phase Separation of Quantum Liquid Mixtures
Prisk, T. R.; Pantalei, C.; Kaiser, H.; Sokol, P. E.
2012-08-01
We report small-angle neutron scattering studies of liquid helium mixtures confined in Mobil Crystalline Material-41 (MCM-41), a porous silica glass with narrow cylindrical nanopores (d=3.4nm). MCM-41 is an ideal model adsorbent for fundamental studies of gas sorption in porous media because its monodisperse pores are arranged in a 2D triangular lattice. The small-angle scattering consists of a series of diffraction peaks whose intensities are determined by how the imbibed liquid fills the pores. Pure He4 adsorbed in the pores show classic, layer-by-layer film growth as a function of pore filling, leaving the long range symmetry of the system intact. In contrast, the adsorption of He3-He4 mixtures produces a structure incommensurate with the pore lattice. Neither capillary condensation nor preferential adsorption of one helium isotope to the pore walls can provide the symmetry-breaking mechanism. The scattering is consistent with the formation of randomly distributed liquid-liquid microdomains ˜2.3nm in size, providing evidence that confinement in a nanometer scale capillary can drive local phase separation in quantum liquid mixtures.