Maximally entangled mixed states made easy
Aiello, A; Voigt, D; Woerdman, J P
2006-01-01
We show that, contrarily to a recent claim [M. Ziman and V. Bu\\v{z}ek, Phys. Rev. A. \\textbf{72}, 052325 (2005)], it is possible to achieve maximally entangled mixed states of two qubits from the singlet state via the action of local nonunital quantum channels. Moreover, we present a simple, feasible linear optical implementation of one of such channels.
Entanglement of spin coherent mixed states
Mansour, Mostafa; Hassouni, Yassine
2016-04-01
In this paper, we quantify the amount of entanglement of bipartite mixed states represented by a statistical mixture of the more general type of two-qubit non-orthogonal states of the form: |ψi>=ui|χi>⊗|ηi>+vi|χi>⊗|ηi‧>+wi|χi‧>⊗|ηi>+zi|χi‧>⊗|ηi‧>, constructed by linearly independent spin coherent states. We use the concurrence as a measure of entanglement and we study its behavior in terms of the amplitudes of SU(2) coherent states.
Maximal entanglement versus entropy for mixed quantum states
Wei, T C; Goldbart, P M; Kwiat, P G; Munro, W J; Verstraete, F; Wei, Tzu-Chieh; Nemoto, Kae; Goldbart, Paul M.; Kwiat, Paul G.; Munro, William J.; Verstraete, Frank
2003-01-01
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy.
Maximally entangled state can be a mixed state
Li, Zong-Guo; Fei, Shao-Ming; Fan, Heng; Liu, W M
2009-01-01
We present mixed maximally entangled states in d\\otimes d' (d'\\geq 2d) spaces. This result is beyond the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states in $d\\otimes d$ systems, for example, they can be used as a resource for faithful teleportation, their local distinguishability property is also the same as the pure states case. On the other hand, one advantage of these mixed maximally entangled states is that the decoherence induced by certain noisy quantum channel does not destroy their entanglement. Thus one party of these mixed states can be sent through this channel to arbitrary distance while still keeping them as a valuable resource for quantum information processing. We also propose a scheme to prepare these states and confirm their advantage in NMR physical system.
Entangled State Representation for Four-Wave Mixing
MA Shan-Jun; LU Hai-Liang; FAN Hong-Yi
2008-01-01
We introduce the entangled state representation to describe the four-wave mixing. We find that the four-wave mixing operator, which engenders the correct input-output field transformation, has a natural representation in the entangled state representation. In this way, we see that the four-wave mixing process not only involves squeezing but also is an entanglement process. This analysis brings convenience to the calculation of quadrature-amplitude measurement for the output state of four-wave mixing process.
Entangled State Representation for Four-Wave Mixing
Ma, Shan-Jun; Lu, Hai-Liang; Fan, Hong-Yi
2008-08-01
We introduce the entangled state representation to describe the four-wave mixing. We find that the four-wave mixing operator, which engenders the correct input-output field transformation, has a natural representation in the entangled state representation. In this way, we see that the four-wave mixing process not only involves squeezing but also is an entanglement process. This analysis brings convenience to the calculation of quadrature-amplitude measurement for the output state of four-wave mixing process.
Entanglement Distillation for Mixed States Using Particle Statistics
HUANG Xiao-Li; CHENG Li-Hong; YI Xue-Xi
2006-01-01
@@ We extend the idea of entanglement concentration protocol for pure states (Phys. Rev. Lett. 88, 187903) to the case of entanglement distillation for mixed states. The scheme works only with particle statistics and local operations, without the need of any other interactions.
Teleportation of Quantum States through Mixed Entangled Pairs
ZHENG Shi-Biao
2006-01-01
@@ We describe a protocol for quantum state teleportation via mixed entangled pairs. With the help of an ancilla,near-perfect teleportation might be achieved. For pure entangled pairs, perfect teleportation might be achieved with a certain probability without using an ancilla. The protocol is generalized to teleportation of multiparticle states and quantum secret sharing.
Average subentropy, coherence and entanglement of random mixed quantum states
Zhang, Lin; Singh, Uttam; Pati, Arun K.
2017-02-01
Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states approaches the maximum value of the subentropy which is attained for the maximally mixed state as we increase the dimension. In the special case of the random mixed states sampled from the induced measure via partial tracing of random bipartite pure states, we establish the typicality of the relative entropy of coherence for random mixed states invoking the concentration of measure phenomenon. Our results also indicate that mixed quantum states are less useful compared to pure quantum states in higher dimension when we extract quantum coherence as a resource. This is because of the fact that average coherence of random mixed states is bounded uniformly, however, the average coherence of random pure states increases with the increasing dimension. As an important application, we establish the typicality of relative entropy of entanglement and distillable entanglement for a specific class of random bipartite mixed states. In particular, most of the random states in this specific class have relative entropy of entanglement and distillable entanglement equal to some fixed number (to within an arbitrary small error), thereby hugely reducing the complexity of computation of these entanglement measures for this specific class of mixed states.
Entanglement capacity of two-qubit unitary operator for rank two mixed states
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.……
Entanglement capacity of two-qubit unitary operator for rank two mixed states
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.
Entangled states close to the maximally mixed state
Hildebrand, Roland
2009-01-01
We give improved upper bounds on the radius of the largest ball of separable states of an m-qubit system around the maximally mixed state. The ratio between the upper bound and the best known lower bound (Hildebrand, quant.ph/0601201) thus shrinks to a constant c = \\sqrt{34/27} ~ 1.122, as opposed to a term of order \\sqrt{m\\log m} for the best upper bound known previously (Aubrun and Szarek, quant.ph/0503221). We give concrete examples of separable states on the boundary to entanglement which realize these upper bounds. As a by-product, we compute the radii of the largest balls that fit into the projective tensor product of four unit balls in R^3 and in the projective tensor product of an arbitrary number of unit balls in R^n for n = 2,4,8.
Entangled mixed-state generation by twin-photon scattering
Puentes, G; Voigt, D; Woerdman, J P
2006-01-01
We report novel experimental results on mixed-state generation by multi-mode scattering of polarization-entangled photons. By using a large variety of scattering media we obtain two markedly different classes of scattered states; namely Werner-like and sub-Werner-like states. Our experimental findings are in excellent agreement with a phenomenological model based upon the description of a scattering process as a quantum map.
Maximally entangled mixed states for qubit-qutrit systems
Mendonça, Paulo E. M. F.; Marchiolli, Marcelo A.; Hedemann, Samuel R.
2017-02-01
We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity P reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.
Huang Li-Yuan; Fang Mao-Fa
2008-01-01
The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of the noisy quantum channel are studied in detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.
Scheme for purifying a general mixed entangled state and its linear optical implementation
董冬; 张延磊; 邹长铃; 邹旭波; 郭光灿
2015-01-01
We propose a scheme for purification of a general mixed entangled state. In this scheme, we start from a large number of general mixed entangled states and end up, after local operation and classical communication, with a smaller number of Bell diagonal states with higher entanglement. In particular, the scheme can purify one maximally entangled state from two entangled pairs prepared in a class of mixed entangled state. Furthermore we propose a linear optical implementation of the present scheme with polarization beam splitters and photon detectors.
Entanglement on mixed stabilizer states: normal forms and reduction procedures
Audenaert, Koenraad M R; Plenio, Martin B [Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom); Institute for Mathematical Sciences, Imperial College London, Exhibition Road, London SW7 2BW (United Kingdom)
2005-08-01
The stabilizer formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of n-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where mixed stabilizer states correspond to projectors on subspaces associated with stabilizer codes. In this paper, we derive efficient reduction procedures to obtain various useful normal forms for stabilizer states. We explicitly prove that these procedures will always converge to the correct result and that these procedures are efficient in that they only require a polynomial number of operations on the generators of the stabilizers. On one hand, we obtain two single-party normal forms. The first, the row-reduced echelon form, is obtained using only permutations and multiplications of generators. This form is useful to calculate partial traces of stabilizer states. The second is the fully reduced form, where the reduction procedure invokes single-qubit operations and CNOT operations as well. This normal form allows for the efficient calculation of the overlap between two stabilizer states, as well as of the Uhlmann fidelity between them, and their Bures distance. On the other hand, we also find a reduction procedure of bipartite stabilizer states, where the operations involved are restricted to be local ones. The two-party normal form thus obtained lays bare a very simple bipartite entanglement structure of stabilizer states. To wit, we prove that every bipartite mixed stabilizer state is locally equivalent to a direct product of a number of maximally entangled states and, potentially, a separable state. As a consequence, using this normal form we can efficiently calculate every reasonable bipartite entanglement measure of mixed stabilizer states.
How entangled are bound entangled states?
Wei, T C; Goldbart, P M; Munro, W J; Wei, Tzu-Chieh; Altepeter, Joseph B.; Goldbart, Paul M.; Munro, William J.
2003-01-01
Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero entanglement to start with. To date, no analytic results reveal the entanglement content of these strange states. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of geometric measure of entanglement and a related quantity. The results are compared with those for the relative entropy of entanglement and the negativity, and plausible lower bounds on the entanglement of formation are given. Along the way, an intriguing example emerges, in which a bipartite mixed state, associated with Smolin's bound entangled state, can be reversibly converted into a bipartite Bell state, and vice versa. Furthermore, for any N-qubit state that is PPT for all bipartite partitionings, there is no violation of the two-setting, three-setting, a...
Quantifying entanglement properties of qudit mixed states with incomplete permutation symmetry
Barasiński, Artur; Nowotarski, Mateusz
2017-04-01
The characterization of entanglement properties in mixed states is important from both a theoretical and a practical point of view. While the estimation of entanglement of bipartite pure states is well established, for mixed states it is a considerably much harder task. The key elements of the mixed-state entanglement theory are given by the exact solutions which sometimes are possible for special states of high symmetry problems. In this paper, we present the exact investigation on the entanglement properties for a five-parameter family of highly symmetric two-qudit mixed states with equal but arbitrary finite local Hilbert space dimension. We achieve this by extensive analysis of various conditions of separability and the entanglement classification with respect to stochastic local operations and classical communication. Furthermore, our results can be used for an arbitrary state by proper application of the proposed twirling operator.
The entanglement or separability of mixed quantum states as a matter of the choice of observables
Pozzana, Iacopo
2012-01-01
In quantum systems, entanglement corresponds to nonclassical correlation of nonlocal observables. Thus, entanglement (or, to the contrary, separability) of a given quantum state is not uniquely determined by properties of the state, but may depend on the choice of the factorization of the algebra of observables. In the present work, we expose and systematize some recently reported results about the possibility to represent a single quantum state as either entangled or separable. We will distinguish in particular the cases of pure and mixed states. For pure states, it has been shown that observables can always be constructed such that any state has any amount of entanglement possible. For mixed states, the situation is more complex and only partial results are known: while it is always possible to choose a factorization such that a state appears separable, a general criterion to determine whether a state can be represented as entangled is not known. These results will be illustrated by several examples, the ph...
On the volume of the set of mixed entangled states
Zyczkowski, K; Sanpera, A; Lewenstein, M; Zyczkowski, Karol; Horodecki, Pawel; Sanpera, Anna; Lewenstein, Maciej
1998-01-01
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, while separability is connected with quantum mixtures. In particular, states of sufficiently low purity are necessarily separable.
On the volume of the set of mixed entangled states, 2
Zyczkowski, K
1999-01-01
The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional quantum systems affects the results obtained. We demonstrate that the link between the purity of the mixed states and the probability of entanglement is not sensitive to the measure chosen. Since the criterion of partial transposition is not sufficient to distinguish all separable states for N > 6, we develop an efficient algorithm to calculate numerically the entanglement of formation of a given mixed quantum state, which allows us to compute the volume of separable states for N=8 and to estimate the volume of the bound entangled states in this case.
On the volume of the set of mixed entangled states II
Zyczkowski, Karol
1999-01-01
The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional quantum systems affects the results obtained. We demonstrate that the link between the purity of the mixed states and the probability of entanglement is not sensitive to the measure chosen. Since the criterion of partial transposition is not sufficient to di...
Completely mixed state is a critical point for three-qubit entanglement
Tamaryan, Sayatnova, E-mail: sayat@mail.yerphi.am [Department of Theoretical Physics, A. Alikhanyan National Laboratory, Yerevan (Armenia)
2011-06-06
Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown that if the reduced density operator of a some qubit is a multiple of the unit operator, than the geometric entanglement measure of the pure three-qubit state is absolutely independent of the polynomial invariants and is a constant for such tripartite states. Hence a one-particle completely mixed state is a critical point for the geometric measure of entanglement. -- Highlights: → Geometric measure of pure three-qubits is expressed in terms of polynomial invariants. → When one Bloch vector is zero the measure is independent of the remaining invariants. → Hence a one-particle completely mixed state is a critical point for the geometric measure. → The existence of the critical points is an inherent feature of the entanglement.
Entanglement of mixed quantum states for qubits and qudit in double photoionization of atoms
Chakraborty, M., E-mail: bminakshi@yahoo.com [Department of Physics, Asansol Girls’ College, Asansol 713304 (India); Sen, S. [Department of Physics, Triveni Devi Bhalotia College, Raniganj 713347 (India)
2015-08-15
Highlights: • We study tripartite entanglement between two electronic qubits and an ionic qudit. • We study bipartite entanglement between any two subsystems of a tripartite system. • We have presented a quantitative application of entangled properties in Neon atom. - Abstract: Quantum entanglement and its paradoxical properties are genuine physical resources for various quantum information tasks like quantum teleportation, quantum cryptography, and quantum computer technology. The physical characteristic of the entanglement of quantum-mechanical states, both for pure and mixed, has been recognized as a central resource in various aspects of quantum information processing. In this article, we study the bipartite entanglement of one electronic qubit along with the ionic qudit and also entanglement between two electronic qubits. The tripartite entanglement properties also have been investigated between two electronic qubits and an ionic qudit. All these studies have been done for the single-step double photoionization from an atom following the absorption of a single photon without observing spin orbit interaction. The dimension of the Hilbert space of the qudit depends upon the electronic state of the residual photoion A{sup 2+}. In absence of SOI, when Russell–Saunders coupling (L–S coupling) is applicable, dimension of the qudit is equal to the spin multiplicity of A{sup 2+}. For estimations of entanglement and mixedness, we consider the Peres–Horodecki condition, concurrence, entanglement of formation, negativity, linear and von Neumann entropies. In case of L–S coupling, all the properties of a qubit–qudit system can be predicted merely with the knowledge of the spins of the target atom and the residual photoion.
Kus, M; Kus, Marek; Zyczkowski, Karol
2001-01-01
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem. In particular we analyze the simplest case of 2 x 2 problem finding a stratification of the 6-D set of N=4 pure states. The set of effectively different states (which cannot be related by local transformations) is one dimensional. It starts at a 3-D manifold of maximally entangled states, cuts generic 5-D manifolds of entangled states (labeled by non-zero values of the entropy of entanglement), and ends at a single 4-D manifold of separable states.
Entanglement swapping of two arbitrarily degraded entangled states
Kirby, Brian T.; Santra, Siddhartha; Malinovsky, Vladimir S.; Brodsky, Michael
2016-07-01
We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.
Are all maximally entangled states pure?
Cavalcanti, D.; Brandão, F. G. S. L.; Terra Cunha, M. O.
2005-10-01
We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of the monogamy of entanglement: we establish the polygamy of entanglement, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system.
Irreversibility for all bound entangled states
Yang, D; Horodecki, R; Synak-Radtke, B; Yang, Dong; Horodecki, Michal; Horodecki, Ryszard; Synak-Radtke, Barbara
2005-01-01
We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all non-distillable entangled states. In this way we solve a long standing problem, of how "real" is entanglement of bound entangled states. Using the new inequality we also prove impossibility of local-cloning and local-deleting of a known entangled state.
Generation of Entangled State and Entanglement Swapping
YE Liu; GUO Guangcan
2002-01-01
A scheme is proposed for the generation of entangled atomic states and a method is presented to produce entangled photon states. It is shown that entanglement can be swapped from atoms to cavities via atom-cavity interaction.
Conditions for Local Entanglement Manipulation from Pure States to Mixed States
梁林梅; 陈平形; 李承祖; 黄明球
2002-01-01
We discuss the transformation from pure states to mixed states in a bipartite system HA (×) HB and provide the sufficient condition for this transformation. We also provide a necessary and sufficient condition for one class of this transformation. Meanwhile, the method of realization for the transformation from pure states to mixed states is also present. Furthermore, we briefly discuss the application.
Generation and Purification of Atomic Entangled States
YANG Ming; SONG Wei; LI Yingqun; SHI Shouhua; CAO Zhuoliang
2004-01-01
@@ Entangled state plays a more and more important role in quantum information, so the generation of entangled state is of scientific value and practical significance.Although the experimental realization of entangled pairs of atoms and polarized photons have been reported recently, the current preparation schemes cannot meet the need of the practical application of entangled state in Quantum Communication and Quantum Computation.At the same time, resulting from the coupling between the quantum systems and its environment, decoherence of the quantum systems is unavoidable, which sets a vital obstacle on the way of the application of entanglement.There exist some entanglement generation and purification schemes, but the range of its application is relative small.So we proposed a more efficient scheme for entanglement generation and purification.The scheme is mainly based on the combination of linear optics and Cavity QED technique.The entanglement generation scheme can entangle two atoms by using MZI plus an optical cavity.Pure maximally entangled atomic states can be generated from product states or mixed states.Using a MZI, we can extract not only two-atom near-maximally entangled states but also four-atom maximally entangled states from less entangled pure or mixed states.
Entanglement of Formation for Quantum States
ZHAO Hui; WANG Zhi-Xi
2007-01-01
We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generalized concurrence. From the monotonicity and convexity the entanglement of formation for a class of high-dimensional mixed states has been calculated analytically.
Upper bound for SL-invariant entanglement measures of mixed states
Osterloh, Andreas
2016-05-01
An algorithm is proposed that serves to handle full-rank density matrices when coming from a lower-rank method to compute the convex roof. This is in order to calculate an upper bound for any polynomial SL-invariant multipartite entanglement measure E . This study exemplifies how this algorithm works based on a method for calculating convex roofs of rank-2 density matrices. It iteratively considers the decompositions of the density matrix into two states each, exploiting the knowledge for the rank-2 case. The algorithm is therefore quasiexact as far as the rank-2 case is concerned, and it also hints where it should include more states in the decomposition of the density matrix. Focusing on the measure of three-way entanglement of qubits (called three-tangle), I show the results the algorithm gives for two states, one of which is the Greenberger-Horne-Zeilinger-Werner (GHZ-W ) state, for which the exact convex roof is known. It overestimates the three-tangle in the state, thereby giving insight into the optimal decomposition the GHZ-W state has. As a proof of principle, I have run the algorithm for the three-tangle on the transverse quantum Ising model. I give qualitative and quantitative arguments why the convex roof should be close to the upper bound found here.
Continuous-variable entanglement distillation of non-Gaussian mixed states
Dong, Ruifang; Lassen, Mikael Østergaard; Heersink, Joel
2010-01-01
Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network...
Deterministically Entangling Two Remote Atomic Ensembles via Light-Atom Mixed Entanglement Swapping.
Liu, Yanhong; Yan, Zhihui; Jia, Xiaojun; Xie, Changde
2016-05-11
Entanglement of two distant macroscopic objects is a key element for implementing large-scale quantum networks consisting of quantum channels and quantum nodes. Entanglement swapping can entangle two spatially separated quantum systems without direct interaction. Here we propose a scheme of deterministically entangling two remote atomic ensembles via continuous-variable entanglement swapping between two independent quantum systems involving light and atoms. Each of two stationary atomic ensembles placed at two remote nodes in a quantum network is prepared to a mixed entangled state of light and atoms respectively. Then, the entanglement swapping is unconditionally implemented between the two prepared quantum systems by means of the balanced homodyne detection of light and the feedback of the measured results. Finally, the established entanglement between two macroscopic atomic ensembles is verified by the inseparability criterion of correlation variances between two anti-Stokes optical beams respectively coming from the two atomic ensembles.
A Peculiar Tripartite Entangled State
黄燕霞; 於亚飞; 詹明生
2003-01-01
We present a scheme to prepare two-atom Einstein-Podolsky-Rosen states and three-atom entangled states via cavity quantum electrodynamics, and it can be realized experimentally. Importantly, we find that in the set of tripartite entangled states prepared by our scheme there is a peculiar tripartite entangled state except the Greenberger-Horne-Zeilinger (GHZ) state. The peculiar tripartite entangled states have double feature of the GHZ state (i.e. T123 ＞ 0) and W state (i.e. the remaining reduce density matrices ρij retain entanglement according to the positive partial transformation (PPT) criterion) simultaneously. However, its entanglement properties are not completely identical either to the GHZ state or to the W state. It is interesting that for peculiar entanglement properties, the remaining reduced density matrices ρij can retain entanglement or disentanglement independently, which can be chosen freely according to our need.
Quantum Entanglement Swapping between Two Multipartite Entangled States
Su, Xiaolong; Tian, Caixing; Deng, Xiaowei; Li, Qiang; Xie, Changde; Peng, Kunchi
2016-12-01
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement results. After entanglement swapping the two independent multipartite entangled states are merged into a large entangled state in which all unmeasured quantum modes are entangled. The entanglement swapping between a tripartite GHZ state and an Einstein-Podolsky-Rosen entangled state is also demonstrated and the dependence of the resultant entanglement on transmission loss is investigated. The presented experiment provides a feasible technical reference for constructing more complicated quantum networks.
On entanglement in neutrino mixing and oscillations
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2010-06-01
We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.
On entanglement in neutrino mixing and oscillations
Blasone, M; De Siena, S; Illuminati, F
2010-01-01
We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.
On Fermionic Entangled State Representation and Fermionic Entangled Wigner Operator
无
2007-01-01
By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product (IWOP) of Fermi operators is used in our discussion.
Entanglement verification of noisy NOON states
Bohmann, M.; Sperling, J.; Vogel, W.
2017-07-01
Entangled quantum states, such as NOON states, are of major importance for quantum technologies due to their quantum-enhanced performance. At the same time, their quantum correlations are relatively vulnerable when they are subjected to imperfections. Therefore, it is crucial to determine under which circumstances their distinct quantum features can be exploited. In this paper, we study the entanglement property of noisy NOON states. This class of states is a generalization of NOON states including various attenuation effects, such as mixing, constant or fluctuating losses, and dephasing. To verify their entanglement, we pursue two strategies: detection-based entanglement witnesses and entanglement quasiprobabilities. Both methods result from our solution of so-called separability eigenvalue equations. In particular, the entanglement quasiprobabilities allow for a full entanglement characterization. As examples of our general treatment, the cases of NOON states subjected to Gaussian dephasing and fluctuating atmospheric losses are explicitly studied. In any correlated fluctuating loss channel, entanglement is found to survive for nonzero transmissivity. In addition, an extension of our approach to multipartite systems is given, and the relation to the quantum-optical nonclassicality in phase space is discussed.
Review of Entangled Coherent States
Sanders, Barry C
2011-01-01
We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics, and mathematical physics. Despite their inherent fragility they have produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they are entanglements of the coherent states, which are in a sense the most classical of all states of a dynamical system.
Gaussian maximally multipartite entangled states
Facchi, Paolo; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio
2009-01-01
We introduce the notion of maximally multipartite entangled states (MMES) in the context of Gaussian continuous variable quantum systems. These are bosonic multipartite states that are maximally entangled over all possible bipartitions of the system. By considering multimode Gaussian states with constrained energy, we show that perfect MMESs, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of MMESs and their frustration for n <= 7.
Entanglement of Superpositions of Orthogonal Maximally Entangled States
ZHANG Dao-Hua; ZHOU Duan-Lu; FAN Heng
2010-01-01
@@ We study the entanglement properties of the superposed state of orthogonal maximally entangled states.It is shown that the superposed state is maximally entangled and the superposed state is separable.The relation between the superposed state and the mutually unbiased state is discussed.
Bound entangled states invariant under Ux
Wang Zhen; Wang Zhi-Xi
2008-01-01
This paper obtains an entangled condition for isotropic-like states by using an atomic map. It constructs a class of bound entangled states from the entangled condition and shows that the partial transposition of the state from the constructed bound entangled class is an edge bound entangled state by using range criterion.
Preparation of entangled squeezed states and quantification of their entanglement
蔡新华; 匡乐满
2002-01-01
We propose a scheme for generating bipartite and multipartite entangled squeezed states via the Jaynes-Cummingsmodel with large detuning. Bipartite entanglement of these entangled states is quantified by the concurrence. We alsouse the N-tangle to compute multipartite entanglement of these multipartite entangled squeezed states. Finally wediscuss two limiting cases which arise from r → oo and r → 0, in which the multipartite entangled squeezed statereduces correspondingly into an N-qubit Greenberger-Horne-Zeilinger state and an N-qubit W state.
Generating entangled superqubit states
Borsten, L; Duff, M J
2014-01-01
We introduce the global unitary supergroup $\\text{UOSp}((3^n+1)/2 | (3^n-1)/2)$ for an $n$-superqubit system, which contains as a subgroup the local unitary supergroup $[\\text{UOSp}(2|1)]^n$. While for $4>n>1$ the bosonic subgroup in $\\text{UOSp}((3^n+1)/2 | (3^n-1)/2)$ does not contain the standard global unitary group $\\text{SU}(2^n)$, it does have an $\\text{USp}(2^n)\\subset\\text{SU}(2^n)$ subgroup which acts transitively on the $n$-qubit subspace, as required for consistency with the conventional multi-qubit framework. For two superqubits the $\\text{UOSp}(5|4)$ action is used to generate entangled states from the "bosonic" separable state $|00>$.
Are all maximally entangled states pure?
Cavalcanti, D; Terra-Cunha, M O
2005-01-01
In this Letter we study if all maximally entangled states are pure through several entanglement monotones. Our conclusions allow us to generalize the idea of monogamy of entanglement. Then we propose a polygamy of entanglement, which express that if a general multipartite state is maximally entangled it is necessarily factorized by any other system.
A new method for quantifying entanglement of multipartite entangled states
Su, Pei-Yuan; Li, Wen-Dong; Ma, Xiao-Ping; Liu, Kai; Wang, Zhao-Ming; Gu, Yong-Jian
2017-08-01
We propose a new way for quantifying entanglement of multipartite entangled states which have a symmetrical structure and can be expressed as valence-bond-solid states. We put forward a new concept `unit.' The entangled state can be decomposed into a series of units or be reconstructed by multiplying the units successively, which simplifies the analyses of multipartite entanglement greatly. We compute and add up the generalized concurrence of each unit to quantify the entanglement of the whole state. We verify that the new method coincides with concurrence for two-partite pure states. We prove that the new method is a good entanglement measure obeying the three necessary conditions for all good entanglement quantification methods. Based on the method, we compute the entanglement of multipartite GHZ, cluster and AKLT states.
Entanglement for All Quantum States
de la Torre, A. C.; Goyeneche, D.; Leitao, L.
2010-01-01
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical…
Teleportation of Squeezed Entangled State
HU Li-Yun; ZHOU Nan-Run
2007-01-01
Based on the coherent entangled state |α, x＞ we introduce the squeezed entangled state (SES). Then we propose a teleportation protocol for the SES by using Einstein-Podolsky-Rosen entangled state |η＞as a quantum channel.The calculation is greatly simplified by virtue of the Schmidt decompositions of both |α, x＞and |η＞. Any bipartite states that can be expanded in terms of |α, x＞may be teleported in this way due to the completeness of |α, x＞.
Entanglement diversion and quantum teleportation of entangled coherent states
Cai Xin-Hua; Guo Jie-Rong; Nie Jian-Jun; Jia Jin-Ping
2006-01-01
The proposals on entanglement diversion and quantum teleportation of entangled coherent states are presented.In these proposals,the entanglement between two coherent states,|α〉and |-α〉,with the same amplitude but a phase difference of π is utilized as a quantum channel.The processes of the entanglement diversion and the teleportation are achieved by using the 5050 symmetric beam splitters,the phase shifters and the photodetectors with the help of classical information.
S.Abdel-Khalek; M.M.A.Ahmed; A-S F.Obada
2011-01-01
We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic field,initially prepared in a coherent state.Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested.The temporal evolution of the negativity,Wehrl entropy,Wehrl phase distribution and field entropy squeezing are investigated.The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy,Wehrl phase distribution and field entropy squeezing.%We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic Reid, initially prepared in a coherent state. Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested. The temporal evolution of the negativity, Wehrl entropy, Wehrl phase distribution and field entropy squeezing are investigated. The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy, Wehrl phase distribution and field entropy squeezing.
The entanglement purification for entangled multi-particle states
Ye, Liu; Guo Guang Can
2002-01-01
We present two purification schemes for nonmaximally entangled states. We first show that two parties, Alice and Bob, start with shared less-entangled three-particle states to probabilistically produce a three-particle Greenberger-Horne-Zeilinger state by Bell state measurements and positive operator valued measure (POVM) or a unitary transformation. Then, by a straightforward generalization of the schemes, the purification of a multi-particle entangled state can be realized. 25 Refs. --- 35 --- AN
Entanglement properties in a system of a pairwise entangled state
Liu Tang-Kun; Cheng Wei-Wen; Shan Chuan-Jia; Gao Yun-Feng; Wang Ji-Suo
2007-01-01
Based on the quantum information theory, this paper has investigated the entanglement properties of a system which is composed of the two entangled two-level atoms interacting with the two-mode entangled coherent fields. The influences of the strength of light field and the two parameters of entanglement between the two-mode fields on the field entropy and on the negative eigenvalues of partial transposition of density matrix are discussed by using numerical calculations. The result shows that the entanglement properties in a system of a pairwise entangled states can be controlled by appropriately choosing the two parameters of entanglement between the two-mode entangled coherent fields and the strength of two light fields respectively.
Entanglement-assisted state discrimination and entanglement preservation
Güngör, Özenç; Turgut, Sadi
2016-09-01
In this paper, the following scenario is considered: there are two qubits possessed by two parties at different locations. Qubits have been prepared in one of a maximum of four, mutually-orthogonal, entangled states and the parties wish to distinguish between the states by using local operations and classical communication. Although in general it is not possible to distinguish between four arbitrary states, the parties can spend some preshared entanglement to achieve perfect discrimination between four qubit states and can also preserve the entanglement of the states after discrimination. This is shown by employing the theory of majorization and the connections between entanglement transformations and state discrimination protocols.
Entanglement and quantum teleportation via decohered tripartite entangled states
Metwally, N., E-mail: nmohamed31@gmail.com
2014-12-15
The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleported state by controlling on Bell measurements, analyzer angle and channel’s strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the decay rate of entanglement and the fidelity of the teleported states are smaller than those depicted for GHZ state.
Entanglement for all quantum states
De la Torre, A C; Goyeneche, D; Leitao, L [IFIMAR, (CONICET-UNMDP) Departamento de Fisica, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata (Argentina)], E-mail: delatorre@mdp.edu.ar, E-mail: dgoyene@mdp.edu.ar, E-mail: lleitao@mdp.edu.ar
2010-03-15
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.
Entanglement for all quantum states
de la Torre, A C; Leitao, L; 10.1088/0143-0807/31/2/010
2010-01-01
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.
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.
Simulating Entangling Unitary Operator Using Non-maximally Entangled States
LI Chun-Xian; WANG Cheng-Zhi; NIE Liu-Ying; LI Jiang-Fan
2009-01-01
We use non-maximally entangled states (NMESs) to simulate an entangling unitary operator (EUO) w/th a certain probability. Given entanglement resources, the probability of the success we achieve is a decreasing function of the parameters of the EUO. Given an EUO, for certain entanglement resources the result is optimal, i.e., the probability obtains a maximal value, and for optimal result higher parameters of the EUO match more amount of entanglement resources. The probability of the success we achieve is higher than the known results under some condition.
Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation
QIAN Xiao-Qing; SONG Tong-Qiang
2006-01-01
We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.
Relativity of pure states entanglement
Zyczkowski, K; Zyczkowski, Karol; Bengtsson, Ingemar
2002-01-01
Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N >= 3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the 'Future', the 'Past' and the set of noncomparable states.
Probabilistic Teleportation of the Three-Particle Entangled State viaEntanglement Swapping
路洪
2001-01-01
A scheme of teleportation of a three-particle entangled state via entanglement swapping is proposed. It is shown that if a two-particle entangled state and a three-particle entangled state (both are not maximum entangled states) are used as quantum channels, probabilistic teleportation of the three-particle entangled state can be realized.
Teleportation for an Ionic Entangled Internal State by Entanglement Swapping
ZHENG Xiao-Juan; FANG Mao-Fa; LIAO Xiang-Ping; CAI Jian-Wu
2006-01-01
@@ We present an effective scheme to teleport an unknown ionic entangled internal state via trapped ions without joint Bell-state measurement. In the constructed quantum channel process, we adopt entanglement swapping to avoid decrease of entanglement during the distribution of particles. Thus our scheme provides new prospects for quantum teleportation over longer distance. The distinct advantages of our scheme are that our scheme is insensitive to heating of vibrational mode and can be generalized to teleport an N-ion electronic entangled GHZ class state. Furthermore, in our scheme the success probability can reach 1.
基于混合纠缠态的概率超密编码%Probabilistic Superdense Coding with Mixed Entangled State
毛多鹭; 李得超
2011-01-01
在理想的超密编码方案中,发送方凭借一个和接收方共享的最大纠缠纯态,可用传送一量子比特来实现传送两经典比特的信息.本文提出了一个凭借混合纠缠态的超密编码方案,并分析了该方案成功传送信息的概率上界.进一步讨论了该类超密编码的通信容量.%Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case in which the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. The upper bound on the probability to do dense coding is analyzed, and then the capability of dense coding is investigated.
Quantum cobwebs: Universal entangling of quantum states
Arun Kumar Pati
2002-08-01
Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA states, local operations and classical communication, we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit state into a multiqubit entangled state.
Efficient entanglement purification for doubly entangled photon state
WANG Chuan; SHENG YuBo; LI XiHan; DENG FuGuo; ZHANG Wei; LONG GuiLu
2009-01-01
In this paper,we present an efficient purification scheme that improves the efficiency of entanglement purification of the recently proposed entanglement purification scheme for doubly entangled photon states(Phys.Rev.A,2008,77:042315).This modified scheme contains the bit-flip error correction where all the photon pairs can be kept while all the bit-flip errors are corrected and the entanglement purification of phase-flip errors where a wavelength conversion process is used.This scheme has the advantage of high efficiency and a much lower minimum fidelity of the original state.It works under existing technology.
Efficient entanglement purification for doubly entangled photon state
无
2009-01-01
In this paper,we present an efficient purification scheme that improves the efficiency of entanglement purification of the recently proposed entanglement purification scheme for doubly entangled photon states (Phys.Rev.A,2008,77:042315).This modified scheme contains the bit-flip error correction where all the photon pairs can be kept while all the bit-flip errors are corrected and the entanglement purification of phase-flip errors where a wavelength conversion process is used.This scheme has the advantage of high efficiency and a much lower minimum fidelity of the original state.It works under existing technology.
Class of PPT bound entangled states associated to almost any set of pure entangled states
Piani, M
2006-01-01
We analyze a class of entangled states for bipartite $d \\otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is very simple and similar to the one of isotropic states: they are a mixture of a separable and a pure entangled state whose supports are orthogonal. Despite such simple structure, in an opportune interval of the mixing parameter their entanglement is not revealed by partial transposition nor by the realignment criterion, i.e. by any permutational criterion in the bipartite setting. In the range in which the states are Positive under Partial Transposition (PPT), they are not distillable; on the other hand, the states in the considered class are provably distillable as soon as they are Nonpositive under Partial Transposition (NPT). The states are associated to any set of more than two pure states. The analysis is extended to the multipartite setting. By an opportune selection...
Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States
K. Berrada; Y. Hassouni; H. Eleuch
2011-01-01
Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states, we find a link to some entanglement measures through some new parameters （amplitudes of coherent states）. Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of entanglement by applying the formalism of Horodecki et al.
Quantum teleportation of entangled squeezed vacuum states
蔡新华
2003-01-01
An optical scheme for probabilistic teleporting entangled squeezed vacuum states (SVS) is proposed. In this scheme,the teleported state is a bipartite entangled SVS,and the quantum channel is a tripartite entangled SVS.The process of the teleportation is achieved by using a 50/50 symmetric beamsplitter and photon detectors with the help of classical information.
Family of nonlocal bound entangled states
Yu, Sixia; Oh, C. H.
2017-03-01
Bound entanglement, being entangled yet not distillable, is essential to our understanding of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we construct this kind of nonlocal bound entangled state for all finite dimensions larger than two, making possible their experimental demonstration in most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.
Experimental Creation of Entanglement Using Separable States
YANG Xiao-Dong; WANG An-Min; MA Xiao-San; XU Feng; YOU Hao; NIU Wan-Qing
2005-01-01
@@ We experimentally demonstrate that the entanglement can be created on two distant particles using separable states. We show that two working particles can share some entanglement, while one ancilla particle always remains separable from the two working particles during the experimental evolution of the system. Our experiment can be viewed as a benchmark to illustrate the idea that no prior entanglement is necessary to create entanglement.
Entanglement in a four-wave mixing process.
Zheng, Zhan; Wang, Hailong; Cheng, Bing; Jing, Jietai
2017-07-15
We investigate different kinds of entanglement in a four-wave mixing process with a degenerate pump. After analyses on means and quantum fluctuations of the three output beams (Stokes, anti-Stokes, and pump), we verify the existence of genuine tripartite entanglement, and quantify bipartite, two-mode, as well as tripartite entanglement with the covariance matrix. We find out that the input pump power and the nonlinear coupling strength are the physical origins to enhance entanglement at a given photon loss.
Squashed entanglement and approximate private states
Wilde, Mark M.
2016-09-01
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it log 2K ) in an ɛ -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only ɛ and log 2K . Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement.
Shifting entanglement from states to observables
Ranade, Kedar [Institut fuer Quantenphysik, Universitaet Ulm, 89069 Ulm (Germany); Harshman, Nathan [Department of Physics, American University, Washington DC (United States); Institut fuer Quantenphysik, Universitaet Ulm, 89069 Ulm (Germany)
2011-07-01
We illustrate that for any pure state on a finite-dimensional Hilbert space we can construct observables that induce a tensor product structure such that the amount of entanglement of the state may take arbitrary values. In particular, we provide an example of how to construct observables on a d-dimensional system such that an arbitrary known pure state can be treated as maximally entangled. In effect, we show how entanglement properties can be shifted from states to observables.
Ground-State Entanglement and Mixture in an XXZ Spin Chain
WANG Cheng-Zhi; LI Chun-Xian; GUO Guang-Can
2005-01-01
@@ We study the pairwise entanglement and mixture of a three-qubit XXZ spin chain in the ground state in thepresence of an external magnetic field B. The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered, and entanglement versus the mixture of all the two-spin states is investigated. We find that the maximal entangled mixed state can be obtained in the considered system by controlling the magnetic field. Our results provide another way to generate maximally entangled mixed states.
Non-Markovianity assisted Steady State Entanglement
Huelga, Susana F; Plenio, Martin B
2011-01-01
We analyze the dependence of steady state entanglement in a dimer system with a coherent exchange interaction and subject to local dephasing on the degree of Markovianity of the system-environment interaction. We demonstrate that non-Markovianity of the system-environment interaction is an essential resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations results in separable steady states. This result illustrates possible mechanisms leading to long lived entanglement in purely decohering local environments. A feasible experimental demonstration of this non-Markovianity assisted steady state entanglement using a system of trapped ions is presented.
Weakly-entangled states are dense and robust
Orus, R; Orus, Roman; Tarrach, Rolf
2004-01-01
Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and non-distillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely bi-separable. Our results are not only restricted to this class of quantum states, since they rest upon very general properties of mixed states and Unextendible Product Bases for any possible number of parties. Robustness against noise of the relevant properties of these states implies the significance of their possible experimental realization, therefore being of physical -and not exclusively mathematical- interest.
Quantum Decoherence for Multi-Photon Entangled States
SUN Yan-Hua; ZHU Xia; KUANG Le-Man
2005-01-01
@@ We investigate quantum decoherence of the multi-photon entangled state |ψNm＞ = Nm[cosγ|N- m＞1|m＞2 +eiθm sinγ|m＞1|N - m＞2]. When the entangled channel |ψNm＞ is embedded in an environment, the channel decoheres and becomes a mixed state governed by a master equation. We calculate thelinear entropy and the relative entropy of entanglement, which describe the mixedness and the amount of entanglement for the mixed state, respectively. We show that quantum decoherence weakens the amount of entanglement and enhances the mixedness with the time evolution. It is indicated that the relative entropy of entanglement depends on not only the initial entanglement angle and the decohering parameter, but also the number of photons in each mode. In particular, we find that the decohering speed depends on the number-difference of photons in the two modes. The larger the number-difference of photons is, the higher the decohering speed.
Separable states can be used to distribute entanglement
Cubitt, T S; Dür, W; Cirac, J I
2003-01-01
We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.
Unitarily localizable entanglement of Gaussian states
Serafini, A; Illuminati, F; Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2004-01-01
We consider generic $m \\times n$-mode bipartitions of continuous variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as $(m+n)$-mode Gaussian states invariant under local mode permutations on the $m$-mode and $n$-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of $m+n-2$ uncorrelated single-mode states. The entanglement between the $m$-mode and the $n$-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of $(m + n)$-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and ...
Quantum repeaters with entangled coherent states
Sangouard, Nicolas; Gisin, Nicolas; Laurat, Julien; Tualle-Brouri, Rosa; Grangier, Philippe
2009-01-01
Entangled coherent states can be prepared remotely by subtracting non-locally a single photon from two quantum superpositions of coherent states, the so-called "Schroedinger's cat" state. Such entanglement can further be distributed over longer distances by successive entanglement swapping operations using linear optics and photon-number resolving detectors. The aim of this paper is to evaluate the performance of this approach to quantum repeaters for long distance quantum communications. Despite many attractive features at first sight, we show that, when using state-of-the-art photon counters and quantum memories, they do not achieve higher entanglement generation rates than repeaters based on single-photon entanglement. We discuss potential developments which may take better advantage of the richness of entanglement based on continuous variables, including in particular efficient parity measurements.
Entangled States and the Gravitational Quantum Well
Alves, Rui; Bertolami, Orfeu
2016-01-01
We study the continuous variable entanglement of a system of two particles under the influence of Earth's gravitational field. We determine a phase-space description of this bipartite system by calculating its Wigner function and verify its entanglement by applying a generalization of the PPT criterion for non-Gaussian states. We also examine the influence of gravity on an idealized entanglement protocol to be shared between stations at different potentials based on the correlation of states of the gravitational quantum well.
Detecting Multiparticle Entanglement of Dicke States
Lücke, Bernd; Peise, Jan; Vitagliano, Giuseppe
2014-01-01
of entangled states, including Dicke states. Experimentally, we produce a Dicke-like state using spin dynamics in a Bose-Einstein condensate. Our criterion proves that it contains at least genuine 28-particle entanglement. We infer a generalized squeezing parameter of −11.4(5) dB....
Entanglement classification with matrix product states
Sanz, M.; Egusquiza, I. L.; di Candia, R.; Saberi, H.; Lamata, L.; Solano, E.
2016-07-01
We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .
Entanglement classification with matrix product states.
Sanz, M; Egusquiza, I L; Di Candia, R; Saberi, H; Lamata, L; Solano, E
2016-07-26
We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .
Detecting multiparticle entanglement of Dicke states.
Lücke, Bernd; Peise, Jan; Vitagliano, Giuseppe; Arlt, Jan; Santos, Luis; Tóth, Géza; Klempt, Carsten
2014-04-18
Recent experiments demonstrate the production of many thousands of neutral atoms entangled in their spin degrees of freedom. We present a criterion for estimating the amount of entanglement based on a measurement of the global spin. It outperforms previous criteria and applies to a wider class of entangled states, including Dicke states. Experimentally, we produce a Dicke-like state using spin dynamics in a Bose-Einstein condensate. Our criterion proves that it contains at least genuine 28-particle entanglement. We infer a generalized squeezing parameter of -11.4(5) dB.
Quantum entanglement in random physical states
Hamma, Alioscia; Zanardi, Paolo
2011-01-01
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body system are not physically accessible. We define physical ensembles of states by acting on random factorized states by a circuit of length k of random and independent unitaries with local support. This simulates an evolution for finite time k generated by a local (time-dependent) Hamiltonian. We apply group theoretic methods to study these statistical ensemble. In particular, we study the typicality of entanglement by means of the purity of the reduced state. We find that for a time k=O(1) the typical purity obeys the area law, while for a time k \\sim O(L) the purity obeys a volume law, with L the linear size of the system. Moreover, we show that for large values of k the reduced state becomes very close to the completely mixed state.
Bipartite and Multipartite Entanglement of Gaussian States
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three-mode Gaussian states, at variance with their discrete-variable counterparts, allow a promiscuous sharing of ...
Teleportation of Two-Particle Entangled State via Cluster State
LI Da-Chuang; CAO Zhuo-Liang
2007-01-01
In this paper,two schemes for teleporting an unknown two-particle entangled state from the sender (Alice)to the receiver (Bob) via a four-particle entangled cluster state are proposed.In these two schemes,the unknown twoparticle entangled state can be teleported perfectly.The successful probabilities and fidelities of the schemes can reach unity.
Measuring the entanglement of bipartite pure states
Sancho, J M
2000-01-01
The problem of the experimental determination of the amount of entanglement of a bipartite pure state is addressed. We show that measuring a single observable does not suffice to determine the entanglement of a given unknown pure state of two particles. Possible minimal local measuring strategies are discussed and a comparison is made on the basis of their best achievable precision.
Algorithmic complexity and entanglement of quantum states.
Mora, Caterina E; Briegel, Hans J
2005-11-11
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.
Diagnosing Topological Edge States via Entanglement Monogamy.
Meichanetzidis, K; Eisert, J; Cirio, M; Lahtinen, V; Pachos, J K
2016-04-01
Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this Letter, we propose an alternative approach to assessing topologically induced edge states in free and interacting fermionic systems. We do so by focussing on the fermionic covariance matrix. This matrix is often tractable either analytically or numerically, and it precisely captures the relevant correlations of the system. By invoking the concept of monogamy of entanglement, we show that highly entangled states supported across a system bipartition are largely disentangled from the rest of the system, thus, usually appearing as gapless edge states. We then define an entanglement qualifier that identifies the presence of topological edge states based purely on correlations present in the ground states. We demonstrate the versatility of this qualifier by applying it to various free and interacting fermionic topological systems.
Increasing Entanglement between Gaussian States by Coherent Photon Subtraction
Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa
2007-01-01
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states w...
Entanglement Witnesses and Characterizing Entanglement Properties of Some PPT States
Jafarizadeh, M A; Akbari, Y
2010-01-01
On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3x3 and 4x4 systems are constructed. In both cases, the constructed EWs correspond to the hyperplanes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).
Classification of Entanglement in Symmetric States
Aulbach, Martin
2011-01-01
Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis the entanglement of symmetric multipartite states is categorised, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalisation of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterisation of entanglement equivalence classes such as Stoc...
Task-oriented maximally entangled states
Agrawal, Pankaj; Pradhan, B, E-mail: agrawal@iopb.res.i, E-mail: bpradhan@iopb.res.i [Institute of Physics, Sachivalaya Marg, Bhubaneswar, Orissa 751 005 (India)
2010-06-11
We introduce the notion of a task-oriented maximally entangled state (TMES). This notion depends on the task for which a quantum state is used as the resource. TMESs are the states that can be used to carry out the task maximally. This concept may be more useful than that of a general maximally entangled state in the case of a multipartite system. We illustrate this idea by giving an operational definition of maximally entangled states on the basis of communication tasks of teleportation and superdense coding. We also give examples and a procedure to obtain such TMESs for n-qubit systems.
Many-particle entanglement criterion for superradiant-like states
Tasgin, Mehmet Emre
2016-01-01
We derive a many-particle inseparability criterion for mixed states using the relation between single-mode and many-particle nonclassicalities. It works very well not only in the vicinity of the Dicke states, but also for the superposition of them: superradiant ground state of finite/infinite number of particles and time evolution of single-photon superradiance. We also obtain a criterion for ensemble-field entanglement which works fine for such kind of states. Even though the collective excitations of the many-particle system is sub-Poissonian --which results in entanglement-- the wave function displays bunching.
Optimized entanglement witnesses for Dicke states
Bergmann, Marcel; Guehne, Otfried [Naturwissenschaftlich-Technische Fakultaet, Universitaet Siegen, Department Physik, Walter-Flex-Strasse 3, D-57068 Siegen (Germany)
2013-07-01
Quantum entanglement is an important resource for applications in quantum information processing like quantum teleportation and cryptography. Moreover, the number of particles that can be entangled experimentally using polarized photons or ion traps has been significantly enlarged. Therefore, criteria to decide the question whether a given multi-particle state is entangled or not have to be improved. Our approach to this problem uses the notion of PPT mixtures which form an approximation to the set of bi-separable states. With this method, entanglement witnesses can be obtained in a natural manner via linear semi-definite programming. In our contribution, we will present analytical results for entanglement witnesses for Dicke states. This allows to overcome the limitations of convex optimization.
Remote State Preparation with Genuine Multipartite Entanglement
MA Yi-Cong; ZHANG Yong-Sheng; GUO Guang-Can
2007-01-01
Enlightened by the work of Yeo and Chua [Phys. Rev. Lett. 96 (2006) 060502] for teleportation and dense coding with genuine multipartite entanglement, we present an explicit protocol for faithful remote state preparation in a real coefficient case by using the same four-particle entangled state which is not reducible to pair of Bell states.It is shown that any complex coefficient case can be changed to a real coefficient case. With this protocol, the state can play an analogous role to Einstein-Podolsky-Rosen pairs in the theory of multipartite entanglement.
Teleportation of N-particle entangled W state via entanglement swapping
Zhan You-Bang
2004-01-01
A scheme for teleporting an unknown N-particle entangled W state is proposed via entanglement swapping. In this scheme, N maximally entangled particle pairs are used as quantum channel. As a special case, the teleportation of an unknown four-particle entangled W state is studied.
Symmetric states: Their nonlocality and entanglement
Wang, Zizhu; Markham, Damian [CNRS LTCI, Département Informatique et Réseaux, Telecom ParisTech, 23 avenue d' Italie, CS 51327, 75214 Paris CEDEX 13 (France)
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
Entanglement as minimal discord over state extensions
Luo, Shunlong
2016-09-01
The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.
Concentration of Unknown Atomic Entangled States via Entanglement Swapping through Raman Interaction
ZOU Jin-Hua; HU Xiang-Ming
2008-01-01
We show that entanglement concentration of unknown atomic entangled states is achieved via the implementation of entanglement swapping based on Raman interaction in cavity QED. A maximally entangled state is obtained from a pair of partially entangled states probabilistically. Due to Raman interaction of two atoms with a cavity mode and an external driving field, the influence of atomic spontaneous emission has been eliminated. Because of the virtual excitation of the cavity mode, the decoherence of cavity decay and thermal field is neglected.
Non-Markovianity-assisted steady state entanglement.
Huelga, Susana F; Rivas, Ángel; Plenio, Martin B
2012-04-20
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.
Tensor eigenvalues and entanglement of symmetric states
Bohnet-Waldraff, F.; Braun, D.; Giraud, O.
2016-10-01
Tensor eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a tensor that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding tensor eigenvalues contain information about the multipartite entanglement (or, equivalently, the quantumness) of the state. This extends previous results connecting entanglement to spectral properties related to the state. We show that if the smallest tensor eigenvalue is negative, the state is detected as entangled. While for spin-1 states the positivity of the smallest tensor eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest tensor eigenvalue.
A field-theoretical approach to entanglement in neutrino mixing and oscillations
Blasone, M; De Siena, S; Illuminati, F
2014-01-01
The phenomena of particle mixing and flavor oscillations in elementary particle physics can be addressed by the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and anti-neutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
Entanglement swapping between atom and cavity and generation of entangled state of cavity fields
Chen Ai-Xi; Deng Li
2007-01-01
This paper proposes a scheme where entanglement swapping between atom and cavity can be realized. A-type three-level atoms interacting resonantly with cavity field are considered. By detecting atom and cavity field, it realizes entanglement swapping between atom and cavity. It uses the technique of entanglement swapping to generate an entangled state of two cavity fields by measuring on atoms. It discusses the experimental feasibility of the proposed scheme and application of entangled state of cavity fields.
Teleportation of Multi-qudit Entangled States
ZHAN Xiao-Gui; LI Hong-Mei; ZENG Hao-Sheng
2006-01-01
@@ We propose a method to realize the teleportation of an unknown entangled state that consists of many qudits through a partially entangled-qudit quantum channel with the help of 2 log2 d-bit classical communication. The operations used in the teleportation process include a generalized Bell-state measurement and a series of singlequdit π-measurements performed by Alice, a series of generalized qudit-Pauli gates and two-level unitary gates,as well as a qubit measurement performed by Bob. For a maximally entangled quantum channel, the successful probability of the teleportation becomes unit.
Entangled States, Holography and Quantum Surfaces
Chapline, G F
2003-08-13
Starting with an elementary discussion of quantum holography, we show that entangled quantum states of qubits provide a ''local'' representation of the global geometry and topology of quantum Riemann surfaces. This representation may play an important role in both mathematics and physics. Indeed, the simplest way to represent the fundamental objects in a ''theory of everything'' may be as muti-qubit entangled states.
Entanglement and the shareability of quantum states
Doherty, Andrew C.
2014-10-01
This brief review discusses the problem of determining whether a given quantum state is separable or entangled. I describe an established approach to this problem that is based on the monogamy of entanglement, which is the observation that a pair of quantum systems that are strongly entangled must be uncorrelated with the rest of the world. Unentangled states on the other hand involve correlations that can be shared with many other parties. Checking whether a given quantum state is shareable involves constructing certain symmetric quantum state extensions and I discuss how to do this using a class of optimizations known as semidefinite programs. An attractive feature of this approach is that it generates explicit entanglement witnesses that can be measured to demonstrate the entanglement experimentally. In recent years analysis of this approach has greatly increased our understanding of the complexity of determining whether a given quantum state is entangled and this review aims to give a unified discussion of these developments. Specifically, I describe how to use finite quantum de Finetti theorems to prove that highly shareable states are nearly separable and use these results to understand the computational complexity of the problem. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.
Entanglement frustration in multimode Gaussian states
Lupo, Cosmo; Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio
2011-01-01
Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low and high energy limit.
Entanglement concentration and teleportation of multipartite entangled states in an ion trap
Pan Chang-Ning; Fang Mao-Fa
2007-01-01
We propose an effective scheme for the entanglement concentration of a four-particle state via entanglement swapping in an ion trap. Taking the maximally entangled state after concentration as a quantum channel, we can faithfully and determinatively teleport quantum entangled states from Alice to Bob without the joint Bell-state measurement. In the process of constructing the quantum channel, we adopt entanglement swapping to avoid the decrease of entanglement during the distribution of particles. Thus our scheme provides a new prospect for quantum teleportation over a longer distance. Furthermore, the success probability of our scheme is 1.0.
Two-Mode Excited Entangled Coherent State: Nonclassicality and Entanglement
Zhang, Hao-Liang; Wu, Jia-Ni; Liu, Cun-Jin; Hu, Yin-Quan; Hu, Li-Yun
2017-03-01
Two-mode excited entangled coherent states (TME-ECSs) are introduced by operating repeatedly the photon-excited operator on the ECSs. It is shown that the normalization constant is related to the product of two Laguerre polynomials. The influence of the operation on nonclassical behaviour of the ECSs is investigated in terms of cross-correlation function, anti-bunching effect and the negativity of Wigner function, which show that nonclassical properties can be enhanced. In addition, inseparability properties of the TME-ECSs are discussed by using Bell inequality and concurrence. It is found that the degree of quantum entanglement of even ECSs increases with the increase of the total excited photon number, and the violation of Bell inequality can be present for both even and odd case only when the total excited photon numbers are even and odd, respectively.
Quantum Entanglement in Neural Network States
Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
2017-04-01
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states has recently become highly desirable in the applications of machine-learning techniques to quantum many-body physics. In this paper, we explore the data structures that encode the physical features in the network states by studying the quantum entanglement properties, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement entropy of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states, we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing quantum states with massive entanglement. Strikingly, the neural-network representation for these states is remarkably efficient, in the sense that the number of nonzero parameters scales only linearly with the system size. We further examine the entanglement properties of generic RBM states by randomly sampling the weight parameters of the RBM. We find that their averaged entanglement entropy obeys volume-law scaling, and the meantime strongly deviates from the Page entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with a long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the
Preserving entanglement under decoherence and sandwiching all separable states
Lockhart, R B; Lockhart, Robert; Steiner, Michael
2000-01-01
Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally entangled states. For an entangled state, E, the constucted neighborhood of entangled states is the region outside two parallel hyperplanes, which sandwich the set of all separable states. The states for which these neighborhoods are largest are the maximally entangled ones. As the number of particles, or the dimensions of the Hilbert spaces for two of the particles increases, the distance between two of the hyperplanes which sandwich the separable states goes to zero. It is easy to decide if a state Q is in the neighborhood of entangled states we construct for an entangled state E. One merely has to check if the trace of EQ is greater than a constant which depends upon E and which we determine.
Topological minimally entangled states via geometric measure
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
Spatial entanglement of nonvacuum Gaussian states
Kiałka, Filip; Ahmadi, Mehdi; Dragan, Andrzej
2016-01-01
The vacuum state of a relativistic quantum field contains entanglement between regions separated by spacelike intervals. Such spatial entanglement can be revealed using an operational method introduced in Ann. Phys. 351, 112 (2014), Phys. Rev. D 91, 016005 (2014). In this approach, a cavity is instantaneously divided into halves by an introduction of an extra perfect mirror. Causal separation of the two regions of the cavity reveals nonlocal spatial correlations present in the field, which ca...
Displacement-enhanced entanglement distillation of single-mode-squeezed entangled states
Tipsmark, Anders; Neergaard-Nielsen, Jonas Schou; Andersen, Ulrik Lund
2013-01-01
It has been shown that entanglement distillation of Gaussian entangled states by means of local photon subtraction can be improved by local Gaussian transformations. Here we show that a similar effect can be expected for the distillation of an asymmetric Gaussian entangled state that is produced...... by a single squeezed beam. We show that for low initial entanglement, our largely simplified protocol generates more entanglement than previous proposed protocols. Furthermore, we show that the distillation scheme also works efficiently on decohered entangled states as well as with a practical photon...
Four-qubit PPT entangled symmetric states
Tura, J; Hyllus, P; Kuś, M; Samsonowicz, J; Lewenstein, M
2012-01-01
We solve an open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical method that allows to construct multipartite PPT entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states. Second, we adapt the algorithm allowing to search for extremal elements in the convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum, Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we search for extremal four-qubit PPTESS and show that generically they have ranks (5,7,8). Finally, we provide an exhaustive characterization of these states with respect to their separability properties.
Entanglement and Coherence in Quantum State Merging.
Streltsov, A; Chitambar, E; Rana, S; Bera, M N; Winter, A; Lewenstein, M
2016-06-17
Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging, where two parties aim to merge their tripartite quantum state parts. In standard quantum state merging, entanglement is considered to be an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.
Entanglement in a Solid State Spin Ensemble
Simmons, Stephanie; Riemann, Helge; Abrosimov, Nikolai V; Becker, Peter; Pohl, Hans-Joachim; Thewalt, Mike L W; Itoh, Kohei M; Morton, John J L
2010-01-01
Entanglement is the quintessential quantum phenomenon and a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing (QIP) and the strongest forms of quantum cryptography. Spin ensembles, such as those in liquid state nuclear magnetic resonance, have been powerful in the development of quantum control methods, however, these demonstrations contained no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered phosphorus-doped silicon. We combined high field/low temperature electron spin resonance (3.4 T, 2.9 K) with hyperpolarisation of the 31P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% compared with the ideal state a...
Teleportations of Mixed States and Multipartite Quantum States
YU Chang-Shui; WANG Ya-Hong; SONG He-Shan
2007-01-01
In this paper, we propose a protocol to deterministically teleport an unknown mixed state of qubit by utilizing a maximally bipartite entangled state of qubits as quantum channel. Ifa non-maximally entangled bipartite pure state is employed as quantum channel, the unknown mixed quantum state of qubit can be teleported with 1 - √1 - C2 probability, where C is the concurrence of the quantum channel. The protocol can also be generalized to teleport a mixed state of qudit or a multipartite mixed state. More important purpose is that, on the basis of the protocol, the teleportation of an arbitrary multipartite (pure or mixed) quantum state can be decomposed into the teleportation of each subsystem by employing separate entangled states as quantum channels. In the case of deterministic teleportation,Bob only needs to perform unitary transformations on his single particles in order to recover the initial teleported multipartite quantum state.
A class of Bell diagonal states and entanglement witnesses
Chruscinski, D; Mlodawski, K; Matsuoka, T
2010-01-01
We analyze special class of bipartite states - so called Bell diagonal states. In particular we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis.
Feynman Path Integrals Over Entangled States
Green, A G; Keeling, J; Simon, S H
2016-01-01
The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral over a sequence of matrix product states. The paths that dominate this path integral include some degree of entanglement. This new feature allows several insights and applications: i. A Ginzburg-Landau description of deconfined phase transitions. ii. The emergence of new classical collective variables in states that are not adiabatically continuous with product states. iii. Features that are captured in product-state field theories by proliferation of instantons are encoded in perturbative fluctuations about entangled saddles. We develop a general formalism for such path integrals and a couple of simple examples to illustrate their utility.
Optimal verification of entanglement in a photonic cluster state experiment
Wunderlich, H; Plenio, M B [Institut fuer Theoretische Physik, Universitaet Ulm, Albert Einstein-Allee 11, 89068 Ulm (Germany); Vallone, G [Centro Studi e Ricerche ' Enrico Fermi' , Via Panisperna 89/A, Compendio del Viminale, Roma 00184 (Italy); Mataloni, P, E-mail: harald.wunderlich@uni-ulm.de [Dipartimento di Fisica della ' Sapienza' Universita di Roma, Roma 00185 (Italy)
2011-03-15
We report on the quantification of entanglement by means of entanglement measures on a four- and a six-qubit cluster state realized by using photons entangled both in polarization and linear momentum. This paper also addresses the question of the scaling of entanglement bounds from incomplete tomographic information on the density matrix under realistic experimental conditions.
Probabilistic Teleportation of a Four-Particle Entangled State
ZHAN You-Bang; FU Hao; DONG Zheng-Chao
2005-01-01
A Scheme for teleporting an unknown four-particle entangled state is proposed via entangled swapping. In this scheme, four pairs of entangled particles are used as quantum channel. It is shown that, if the four pairs of particles are nonmaximally entangled, the teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations.
Positive finite rank elementary operators and characterizing entanglement of states
Qi, Xiaofei
2010-01-01
In this paper, a class of indecomposable positive finite rank elementary operators are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of any dimension in terms of two low rank positive elementary operators and get some new mixed entangled states that can not be detected by the positive partial transpose (PPT) criterion and the realignment criterion.
Positive finite rank elementary operators and characterizing entanglement of states
Qi Xiaofei [Department of Mathematics, Shanxi University, Taiyuan 030006 (China); Hou Jinchuan, E-mail: qixf1980@126.com, E-mail: jinchuanhou@yahoo.com.cn [Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024 (China)
2011-05-27
In this paper, some indecomposable positive finite rank elementary operators of order (n, n) are constructed. This allows us to give a simple necessary and sufficient criterion for the separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order (2, 2) and obtain some new mixed entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.
Charcterization of multipartite entanglement
Chong, Bo
2006-06-23
In this thesis, we discuss several aspects of the characterization of entanglement in multipartite quantum systems, including detection, classification and quantification of entanglement. First, we discuss triqubit pure entanglement and propose a special true tripartite entanglement, the mixed entanglement, besides the Greenberger-Horne-Zeilinger (GHZ) entanglement and the W entanglement. Then, based on quantitative complementarity relations, we draw entanglement Venn diagrams for triqubit pure states with different entanglements and introduce the total tangle {tau}{sup (T)} to quantify total entanglement of triqubit pure states by defining the union I that is equivalent to the total tangle {tau}{sup (T)} from the mathematical point of view. The generalizations of entanglement Venn diagrams and the union I to N-qubit pure states are also discussed. Finally, based on the ranks of reduced density matrices, we discuss the separability of multiparticle arbitrary-dimensional pure and mixed states, respectively. (orig.)
姚春梅; 李敏; 叶柳; 郭光灿
2002-01-01
We discuss two different schemes for the probabilistic preparation of N-particle cat states using pure multiparticle entangled states via entanglement swapping and entanglement concentration. At the centre of distribution A,Alice performs all of the operations required to achieve our goal.
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
Delayed birth of distillable entanglement in the evolution of bound entangled states
Derkacz, Łukasz
2010-01-01
The dynamical creation of entanglement between three-level atoms coupled to the common vacuum is investigated. For the class of bound entangled initial states we show that the dynamics of closely separated atoms generates stationary distillable entanglement of asymptotic states. We also find that the effect of delayed sudden birth of distillable entanglement occurs in the case of atoms separated by a distance comparable with the radiation wavelength.
Engineering of Multi-Dimensional Entangled States of Photon Pairs Using Hyper-Entanglement
REN Xi-Feng; GUO Guo-Ping; LI Jian; LI Chuan-Feng; GUO Guang-Can
2006-01-01
@@ Multi-dimensional entangled states have been proven to be more powerful in some quantum information processes.Down-converted photons from spontaneous parametric down-conversion are used to engineer multi-dimensional entangled states. A kind of multi-degree multi-dimensional Greenberger-Horne-Zeilinger states can also be generated. The hyper-entangled photons are entangled in energy-time, polarization and orbital angular momentum,which is proven to be useful to increase the dimension of systems and to investigate higher-dimensional entangled states.
戴宏毅; 李承祖; 陈平形
2003-01-01
We present a scheme to teleport an unknown three-particle entangled state from a sender to either one of two receivers. The partial three-particle entangled state and the three-particle entangled W state are considered as the quantum channels. An unknown three-particle entangled state can be perfectly teleported probabilistically by performing two generalized Bell measurements and the Hadamard operation at the sender's side and introducing an appropriate unitary transformation in each receiver's laboratory conditioned on the simple measurement outcome of the other. All kinds of unitary transformations are given in details. This scheme can be directly generalized to teleport an unknown three-particle entangled state from a sender to any one of N receivers by the partial three-particle entangled state and the (N + 1)-particle entangled W state.
Two-mode excited entangled coherent states and their entanglement properties
Zhou Dong-Lin; Kuang Le-Man
2009-01-01
This paper introduces two types of two-mode excited entangled coherent states(TMEECSs)|Ψ±(α,m,n)>,studies their entanglement characteristics,and investigates the influence of photon excitations on quantum entanglement.It shows that for the state|Ψ+(α,m,m)>the two-mode photon excitations affect seriously entanglement character while the state |Ψ-(α,m,m)>is always a maximally entangled state,and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements.It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.
Quantum Teleportation of a Three-Particle Entangled State
刘金明; 郭光灿
2002-01-01
We present a scheme for teleporting a three-particle entangled state to three remote particles. In this scheme, three pairs of pure nonmaximally entangled states are considered as quantum channels. It is found that by means of optimal discrimination between two nonorthogonal quantum states, probabilistic teleportation of the three-particle entangled state can be achieved.
Entanglement sharing: from qubits to Gaussian states
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such {\\em monogamy constraints} have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In these proceedings we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of $N$ qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.
Entanglement Preserving in Quantum Copying of Three－Qubit Entangled State
TONGZhao－Yang; KUANGLe－Man
2002-01-01
We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes,respectively,and investigate iterating quantum copying for the three-qubit system.There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine.we also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process.We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement,and output state via non-local cloning exhiits the fidelity better than local cloning.
Remarks on entanglement measures and non-local state distinguishability
Eisert, J [QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom); Audenaert, K [QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom); Plenio, M B [QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom)
2003-05-23
We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we concentrate on the relative entropy of entanglement with reversed entries. We show that this quantity is an entanglement monotone which is strongly additive, thereby demonstrating that monotonicity under local quantum operations and strong additivity are compatible in principle. In accordance with the presented statistical interpretation which is provided, this entanglement monotone, however, has the property that it diverges on pure states, with the consequence that it cannot distinguish the degree of entanglement of different pure states. We also prove that the relative entropy of entanglement with respect to the set of disentangled states that have identical reductions to the primary state is an entanglement monotone. We finally investigate the trace-norm measure and demonstrate that it is also a proper entanglement monotone.
Assadi, Leila; Jafarpour, Mojtaba
2016-07-01
We use concurrence to study bipartite entanglement, Meyer-Wallach measure and its generalizations to study multi-partite entanglement and MABK and SASA inequalities to study the non-local properties of the 4-qubit entangled graph states, quantitatively. Then, we present 3 classifications, each one in accordance with one of the aforementioned properties. We also observe that the classification according to multipartite entanglement does exactly coincide with that according to nonlocal properties, but does not match with that according to bipartite entanglement. This observation signifies the fact that non-locality and multipartite entanglement enjoy the same basic underlying principles, while bipartite entanglement may not reveal the non-locality issue in its entirety.
Entanglement purification of unknown quantum states
Brun, Todd A.; Caves, Carlton M.; Schack, Rüdiger
2001-04-01
A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance, in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state ρ(N) of the N copies of the quantum system is exchangeable, one can write down a simple general expression for ρ(N). By measuring one or more of the subsystems, one can gain information and update the state estimate for the remaining subsystems with the quantum version of the Bayes rule. Using this rule, we show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.
TELEPORTATION OF A TWO-PARTICLE ENTANGLED STATE
叶柳; 姚春梅; 郭光灿
2001-01-01
A scheme for teleporting a two-particle entangled state via a three-particle entangled state is proposed. It is shown that the probability of successful teleportation is twice the modulus square of the smaller Schmidt coefficient of the entangled three-particle state.
Tractable Quantification of Entanglement for Multipartite Pure States
JIANG Nian-Quan; WANG Yu-Jian; ZHENG Yi-Zhuang; CAI Gen-Chang
2008-01-01
We present kth-order entanglement measure and global kth-order entanglement measure for multipartite pure states, and extend Bennett's measure of partial entropy for bipartite pure states to a multipartite case. These measures are computable and can effectively classify and quantify the entanglement of multipartite pure states.
Presentation Entanglement states and its application in quantum computation
Yadollah Farahmand
2014-06-01
Full Text Available In this article we will consider the entanglement states and we will formulate the density matrix and the expectation value of entanglement state to mathematics and also we will explain the applications of entanglement states in superdense coding and sending information ( qubits transfer.
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 ...
Experimental entanglement distillation of mesoscopic quantum states
Dong, Ruifang; Lassen, Mikael Østergaard; Heersink, Joel
2008-01-01
The distribution of entangled states between distant parties in an optical network is crucial for the successful implementation of various quantum communication protocols such as quantum cryptography, teleportation and dense coding(1-3). However, owing to the unavoidable loss in any real optical...
Increasing entanglement between Gaussian states by coherent photon subtraction.
Ourjoumtsev, Alexei; Dantan, Aurélien; Tualle-Brouri, Rosa; Grangier, Philippe
2007-01-19
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states with negative Wigner functions and complex structures more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.
Increasing entanglement between Gaussian states by coherent photon subtraction
Ourjoumtsev, A; Tualle-Brouri, R; Grangier, P; Ourjoumtsev, Alexei; Dantan, Aurelien; Tualle-Brouri, Rosa; Grangier, Philippe
2006-01-01
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a non-degenerate parametric amplifier, produces delocalized "Schroedinger kitten" states with complex negative Wigner functions, more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.
Entanglement and double occupancy in many-electron states
Subrahmanyam, V., E-mail: vmani@iitk.ac.i [Department of Physics, Indian Institute of Technology, Kanpur 208016 (India)
2010-07-12
The entanglement in many-electron states is investigated using a global entanglement measure, viz. average site mixedness. We have examined metallic states of noninteracting electrons, Nagaoka and Gutzwiller states of strongly-correlated electrons, and superconducting states. Uncorrelated metallic states at half filling seem to maximize entanglement, as these states optimize the number of holes, the number of doubly-occupied sites. Entanglement is calculated explicitly for Gutzwiller-projected many-electron states in one dimension, which have less entanglement as double occupancy is inhibited in these states. Entanglement in superconducting states, which tend to promote double occupancy, is calculated as a function of the energy gap, and found to be lower than the metallic state entanglement. There is a possibility of a regime with a nonzero single-site concurrence depending on the energy gap.
Entanglement distillation for three-particle W class states
Cao, Z L; Cao, Zhuo-Liang; Yang, Ming
2003-01-01
In this paper, we propose two general entanglement distillation protocols, which can concentrate the non-maximally entangled pure W class state. The general protocols are mainly based on the unitary transformation on the auxiliary particle and one of the three entangled particles, and in the second protocol, the entanglement distillation includes two meanings, namely, extracting the concentrated tripartite entangled W state and obtaining the maximally entangled bipartite state from the garbage state, which gives no contribution to the distillation of non-maximally entangled pure W class state. We can make use of the garbage in the distillation process, and make the entanglement waste in quantum communication as small as possible. A feasible physical scheme is suggested based on the cavity QED.
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 and coherence in quantum state merging
Streltsov, A; Rana, S; Bera, M N; Winter, A; Lewenstein, M
2016-01-01
Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging where two parties aim to merge their parts of a tripartite quantum state. In standard quantum state merging, entanglement is considered as an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process, and apply them to several relevant scenarios. While quantum state merging can lead to ...
Detecting entanglement of states by entries of their density matrices
Qi, Xiaofei
2010-01-01
For any bipartite systems, a universal entanglement witness of rank-4 for pure states is obtained and a class of finite rank entanglement witnesses is constructed. In addition, a method of detecting entanglement of a state only by entries of its density matrix is obtained.
Teleportation of a three-particle entangled W state
郑亦庄; 顾永建; 郭光灿
2002-01-01
We have investigated the problem of teleporting a three-particle entangled W state and we propose a scheme based on entanglement swapping to complete the teleportation. We also put forward a scheme for the teleportation of a general W state by using nonmaximally entangled quantum channels. The probability of success of the latter scheme is obtained.
Probabilistic Teleportation of an Arbitrary n-Particle Entangled State
XI Yong-Jun; FANG Jian-Xing; ZHU Shi-Qun; GUO Zhan-Ying
2005-01-01
A scheme for teleporting an arbitrary n-particle entangled state via n pairs of non-maximally entangled states is proposed. The probability of successful teleportation is determined only by the smaller coefficients of the partially entangled pairs. The method is very easy to be realized.
Entanglement Preserving in Quantum Copying of Three-Qubit Entangled State
TONG Zhao-Yang; KUANG Le-Man
2002-01-01
We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.
Measurement induced chaos with entangled states
Kiss, T; Tóth, L D; Gábris, A; Jex, I; Alber, G
2011-01-01
Quantum control, in a broad sense, may include measurement of quantum systems and, as a feed back operation, selection from an ensemble conditioned on the measurements. The resulting dynamics can be nonlinear and, if applied iteratively, can lead to true chaos in a quantum system. We consider the dynamics of an ensemble of two qubit systems subjected to measurement and conditional selection. We prove that the iterative dynamics leads to true chaos in the entanglement of the qubits. A class of special initial states exhibits high sensitivity to the initial conditions. In the parameter space of the special initial states we identify two types of islands: one converging to a separable state, while the other being asymptotically completely entangled. The islands form a fractal like structure. Adding noise to the initial state introduces a further stable asymptotic cycle.
Multiple teleportation via partially entangled GHZ state
Xiong, Pei-Ying; Yu, Xu-Tao; Zhan, Hai-Tao; Zhang, Zai-Chen
2016-08-01
Quantum teleportation is important for quantum communication. We propose a protocol that uses a partially entangled Greenberger-Horne-Zeilinger (GHZ) state for single hop teleportation. Quantum teleportation will succeed if the sender makes a Bell state measurement, and the receiver performs the Hadamard gate operation, applies appropriate Pauli operators, introduces an auxiliary particle, and applies the corresponding unitary matrix to recover the transmitted state.We also present a protocol to realize multiple teleportation of partially entangled GHZ state without an auxiliary particle. We show that the success probability of the teleportation is always 0 when the number of teleportations is odd. In order to improve the success probability of a multihop, we introduce the method used in our single hop teleportation, thus proposing a multiple teleportation protocol using auxiliary particles and a unitary matrix. The final success probability is shown to be improved significantly for the method without auxiliary particles for both an odd or even number of teleportations.
Exact fluctuation-entanglement relation for bipartite pure states
Villaruel, Aura Mae B
2015-01-01
We identify a subsystem fluctuation (variance) that measures entanglement in an arbitrary bipartite pure state. This fluctuation is of an observable that generalizes the notion of polarization to an arbitrary N-level subsystem. We express this polarization fluctuation in terms of the order-2 Renyi entanglement entropy and a generalized concurrence. The fluctuation-entanglement relation presented here establishes a framework for experimentally measuring entanglement using Stern-Gerlach-type state selectors.
Entanglement distillation between solid-state quantum network nodes
Kalb, N.; Reiserer, A. A.; Humphreys, P. C.; Bakermans, J. J. W.; Kamerling, S. J.; Nickerson, N. H.; Benjamin, S. C.; Twitchen, D. J.; Markham, M.; Hanson, R.
2017-06-01
The impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable imperfections necessitate a means to improve remote entanglement by local quantum operations. We realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. The heralded generation of two copies of a remote entangled state is demonstrated through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. The key combination of generating, storing, and processing entangled states should enable the exploration of multiparticle entanglement on an extended quantum network.
Teleportation of N-Particle Entangled GHZ State via Entanglement Swapping
SHA Jin-Qiao; FANG Jian-Xing; ZHU Shi-Qun; JIANG Wei-Xing; QIAN Xue-Min
2006-01-01
In this scheme, N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N-particle entangled GHZ state via entanglement swapping. In order to realize this teleportation, the sender Alice operates Bell-state measurement on particles belonging to herself. Then she informs the results to the receiver Bob through classical communication. According to the results, Bob operates corresponding transformation to reconstruct the initial state. The advantage of this scheme is that it needs only one common unitary matrix for Alice's different results, which has a more general meaning. As a special case, teleporting an unknown three-particle entangled GHZ state is proposed.
Negative Correlations and Entanglement in Higher-Spin Dicke States
Wang, Xiaoqian; Zhong, Wei; Wang, Xiaoguang
2016-10-01
We consider entanglement criteria based on the spin squeezing inequalities for arbitrary spin systems. Here we use the negative correlations to detect the entanglement in the system with exchange symmetry. For arbitrary spin systems, we can find that the state is entangled, when the minimal pairwise correlation is negative. Then we give a parameter which is defined by the collective angular momentum operator, to detect the entanglement for the Dicke state with N spin -1 particles, and the results are as the same as negative correlation. We also consider the directions of negative correlation, the state is entangled in two orthogonal directions for the superposition of Dicke state without parity.
Comparison of quantum discord and fully entangled fraction of two classes of d⊗ d^2 states
Behdani, Javad; Akhtarshenas, Seyed Javad; Sarbishaei, Mohsen
2017-01-01
The quantumness of a generic state is the resource of many applications in quantum information theory, and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work, we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the d⊗ d Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.
Quantum Discord and Entanglement of Quasi-Werner States Based on Bipartite Entangled Coherent States
Mishra, Manoj K.; Maurya, Ajay K.; Prakash, Hari
2016-06-01
Present work is an attempt to compare quantum discord and quantum entanglement of quasi-Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, the quasi-Werner states based on maximally ECS due to its invariant nature under local operation is independent of measurement basis and mean photon numbers, while for quasi-Werner states based on non-maximally ECS, it depends upon measurement basis as well as on mean photon number. However, for large mean photon numbers since non-maximally ECS becomes almost maximally entangled therefore dependence of quantum discord for non-maximally ECS based quasi-Werner states on the measurement basis disappears.
Trail, Collin M; Madhok, Vaibhav; Deutsch, Ivan H
2008-10-01
We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled tops, where chaos and entanglement arise from the same physical mechanism. The long-time-averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section--it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudorandom states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time-averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble.
On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation
FAN Hong-Yi; JIANG Nian-Quan
2003-01-01
Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.
Probabilistic teleportation of a two-particle entangled state via a partially entangled pair
CHEN Xiu-bo; LIU Xin-yuan; WEN Qiao-yan; ZHU Fu-chen
2006-01-01
A scheme for teleporting an unknown two-particle entangled state is proposed. In comparison with the recent protocol (Cola et al., Phys. Lett. A 337 (2005)), the entangled state as quantum channel required by this scheme is a single,partially entangled pair, which is much easier to prepare and maintain. Furthermore, a positive operator valued measure (POVM) is adopted and all kinds of transformations performed by sender and receiver are given in detail. It is shown that the probability of successful teleportation is twice the modulus square of the smaller Schmidt coefficient of the two-particle entangled state, and the fidelity can reach one.
Cosmological Consequences of Initial State Entanglement
Albrecht, Andreas; Holman, R
2014-01-01
We explore the cosmological consequences of having the fluctuations of the inflaton field entangled with those of another scalar, within the context of a toy model consisting of non-interacting, minimally coupled scalars in a fixed de Sitter background. We find that despite the lack of interactions in the Lagrangian, the initial state entanglement modifies the mode equation for the inflaton fluctuations and thus can induce changes in cosmological observables. These effects are examined for a variety of choices of masses and we find that they can be consistent with the requirement that the back reaction of the modified state not affect the inflationary phase while still giving rise to observable effects in the power spectrum. Our results suggest that more realistic extensions of the ideas explored here beyond the simple toy model may lead to interesting observable effects.
Quantum Enhanced Imaging by Entangled States
2009-07-01
REMOTE SENSING; LIDAR ; RADAR; SYNTHETIC APERTURE RADAR (SAR); SENSORS USING PHOTONS IN A NON- CLASSICAL STATE; EG SQUEEZED, ENTANGLED 16. SECURITY...idler photodetectors are ηs and ηi, respectively, we have, for the number of coincidence counts, islocalwaypairccoinc fN ηηηημ −= 2 . (13...in the square root comes from the beam splitter relation for photons incident on an inefficient photodetector in the quantum model of direct
Quantum Gravity, CPT symmetry and Entangled States
Mavromatos, Nick E
2008-01-01
There may unique ("smoking-gun") signatures of the breakdown of CPT symmetry, induced in some models of Quantum Gravity entailing decoherence for quantum matter. Such effects can be observed in entangled states of neutral mesons via modifications of the respective Einstein-Podolsky-Rosen (EPR) correlators ("omega"-effect). In the talk I discuss experimental signatures and bounds of the omega-effect in Phi- and B-factories, and argue that the effect might be falsifiable at the next generation facilities.
Effect of Dzialoshinski-Moriya interaction on thermal entanglement of a mixed-spin chain
2008-01-01
The effect of Dzialoshinski-Moriya (DM) interaction on thermal entanglement of a mixed-spin chain in an external magnetic field is investigated. It is found that DM interaction may enhance quantum thermal entanglement to a maximal value even though the magnetic field plays a positive role in shrinking thermal entanglement in the mixed-spin chain. Furthermore, the effect of inhomogeneity of the magnetic field on quantum entanglement is analyzed. Our analysis will shed some light on the understanding of the effect of the DM interaction on thermal entanglement of a mixed-spin chain.
Preparation of Entangled States of Three Particles by Adiabatic Passage
郭建友
2002-01-01
We propose a novel technique for the creation of entangled states of three particles, based upon an adiabatic passage induced by a suitably crafted time-dependent external field. We derive the corresponding adiabatic and bare conditions for the preparation of entangled states. We obtain the time evolutions of the energy of the system and the populations involving the initial state and target entangled state.
Heralded generation of a micro-macro entangled state
Andersen, Ulrik Lund; Neergaard-Nielsen, Jonas Schou
2013-01-01
Using different optical setups based on squeezed state and photon subtraction we show how optical entanglement between a macroscopic and a microscopic state-the so-called Schro¨dinger cat state or micro-macro state-can be generated. The entangled state is heralded and is thus produced a priori...
Entangled state fusion with Rydberg atoms
Ji, Y. Q.; Dai, C. M.; Shao, X. Q.; Yi, X. X.
2017-10-01
We propose a scheme for preparation of large-scale entangled GHZ states and W states with neutral Rydberg atoms. The scheme mainly depends on Rydberg antiblockade effect, i.e., as the Rydberg-Rydberg interaction strength and the detuning between the atom transition frequency and the classical laser frequency satisfies some certain conditions, the effective Rabi oscillation between the two ground states and the two excitation Rydberg states would be generated. The prominent advantage is that both two multiparticle GHZ states and two multiparticle W states can be fused in this model, especially the success probability for fusion of GHZ states can reach unit. In addition, the imperfections induced by the spontaneous emission is also discussed through numerical simulation.
Maximally entangled states in pseudo-telepathy games
Mančinska, Laura
2015-01-01
A pseudo-telepathy game is a nonlocal game which can be won with probability one using some finite-dimensional quantum strategy but not using a classical one. Our central question is whether there exist two-party pseudo-telepathy games which cannot be won with probability one using a maximally entangled state. Towards answering this question, we develop conditions under which maximally entangled states suffice. In particular, we show that maximally entangled states suffice for weak projection...
Entangled States Used in Remote Information Concentration and Their Properties
CHEN Yin-Hua; YU Ya-Fei; ZHANG Zhi-Ming
2006-01-01
We analyse a process of remote information concentration achieved by the W state. The result turns out to be neither as good as performed by the GHZ state nor as by the Smolin bound entangled state. Based on this particular phenomenon, the properties of the three entangled states are realized.
Entanglement bounds for squeezed non-symmetric thermal state
Jiang, L
2003-01-01
I study the three parameters bipartite quantum Gaussian state called squeezed asymmetric thermal state, calculate Gaussian entanglement of formation analytically and the up bound of relative entropy of entanglement, compare them with coherent information of the state. Based on the result obtained, it is anticipated that hashing inequality is not violated for squeezed non-symmetric thermal state.
Generation of tripartite entanglement from cascaded four-wave mixing processes.
Wang, Hailong; Zheng, Zhan; Wang, Yaxian; Jing, Jietai
2016-10-03
We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.
Limitations to sharing entanglement
Kim, Jeong San; Sanders, Barry C
2011-01-01
We discuss limitations to sharing entanglement known as monogamy of entanglement. Our pedagogical approach commences with simple examples of limited entanglement sharing for pure three-qubit states and progresses to the more general case of mixed-state monogamy relations with multiple qudits.
Relationship between squeezing and entangled state transformations
Fan Hong Yi
2003-01-01
We show that c-number dilation transform in the Einstein-Podolsky-Rosen (EPR) entangled state, i.e. vertical bar eta sub 1 , eta sub 2) -> vertical bar eta sub 1 , eta sub 2 /mu) (or vertical bar eta sub 1 , eta sub 2) -> vertical bar eta sub 1 /mu, eta sub 2)), maps onto a kind of one-sided two-mode squeezing operator exp left brace i lambda/2(P sub 1 + P sub 2)(Q sub 1 + Q sub 2) - lambda/2 right brace, (or exp left brace i lambda/2(P sub 1 - P sub 2)(Q sub 1 - Q sub 2) - lambda/2 right brace). Using the IWOP technique, we derive their normally ordered form and construct the corresponding squeezed states. In doing so, some new relationship between squeezing and entangled state transformation is revealed. The dynamic Hamiltonian for such a kind of squeezing evolution is derived. The properties and application of the one-sided squeezed state are briefly discussed. These states can also be obtained with the use of a beam splitter.
Multipartite entanglement accumulation in quantum states: Localizable generalized geometric measure
Sadhukhan, Debasis; Roy, Sudipto Singha; Pal, Amit Kumar; Rakshit, Debraj; SenDe, Aditi; Sen, Ujjwal
2017-02-01
Multiparty quantum states are useful for a variety of quantum information and computation protocols. We define a multiparty entanglement measure based on local measurements on a multiparty quantum state and an entanglement measure averaged on the postmeasurement ensemble. Using the generalized geometric measure as the measure of multipartite entanglement for the ensemble, we demonstrate, in the case of several well-known classes of multipartite pure states, that the localized multipartite entanglement can exceed the entanglement present in the original state. We also show that measurement over multiple parties may be beneficial in enhancing localizable multipartite entanglement. We point out that localizable generalized geometric measure faithfully signals quantum critical phenomena in well-known quantum spin models even when considerable finite-size effect is present in the system.
Preparing entangled states by Lyapunov control
Shi, Z. C.; Wang, L. C.; Yi, X. X.
2016-09-01
By Lyapunov control, we present a protocol to prepare entangled states such as Bell states in the context of cavity QED system. The advantage of our method is of threefold. Firstly, we can only control the phase of classical fields to complete the preparation process. Secondly, the evolution time is sharply shortened when compared to adiabatic control. Thirdly, the final state is steady after removing control fields. The influence of decoherence caused by the atomic spontaneous emission and the cavity decay is discussed. The numerical results show that the control scheme is immune to decoherence, especially for the atomic spontaneous emission from |2rangle to |1rangle . This can be understood as the state staying in an invariant subspace. Finally, we generalize this method in preparation of W state.
Preparing entangled states by Lyapunov control
Shi, Z. C.; Wang, L. C.; Yi, X. X.
2016-12-01
By Lyapunov control, we present a protocol to prepare entangled states such as Bell states in the context of cavity QED system. The advantage of our method is of threefold. Firstly, we can only control the phase of classical fields to complete the preparation process. Secondly, the evolution time is sharply shortened when compared to adiabatic control. Thirdly, the final state is steady after removing control fields. The influence of decoherence caused by the atomic spontaneous emission and the cavity decay is discussed. The numerical results show that the control scheme is immune to decoherence, especially for the atomic spontaneous emission from |2rangle to |1rangle . This can be understood as the state staying in an invariant subspace. Finally, we generalize this method in preparation of W state.
Generation of Multiphoton Entangled States with Linear Optical Elements
SHENG Yu-Bo; DENG Fu-Guo; ZHOU Hong-Yu
2008-01-01
We propose a linear optical protocol to generate three-photon and four-photon entangled states without resorting to entangled sources. The setup in this protocol is composed of three beam splitters and two half-wave plates.We can obtain three-photon and four-photon entangled states with postselection, as with other protocols. This protocol has the advantage of high efficiency and is more feasible than others.
Enhancement of entanglement using cascaded four-wave mixing processes.
Xin, Jun; Qi, Jian; Jing, Jietai
2017-01-15
A maximal joint quadrature squeezing of -6.8±0.4 dB is experimentally obtained by a scheme of cascaded four-wave mixing (FWM) processes, which gives strong proof about the inseparability or entanglement between output of the twin beams from the system. Here joint quadrature is the difference between the two quadratures of the twin beam output from the cascaded FWM processes. This result is enhanced by about 3.1 dB, compared with the one of the single FWM process. We also study the gain dependence of the entanglement enhancement in this cascaded system. Theoretical predictions with the considerations of the losses in the experiment are also studied, and a similar trend in the low-gain regime can be found between the experimental results and the theoretical predictions. The scheme of cascaded FWM processes, which can be used to improve or even manipulate the degree of the entanglement between the output fields from the single FWM process, may find its applications in the continuous-variable quantum communication protocols.
Entanglement-fluctuation relation for bipartite pure states
Villaruel, Aura Mae B.; Paraan, Francis N. C.
2016-08-01
We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N -level subsystem. We express this polarization fluctuation in terms of subsystem purity and other entanglement measures. The derived entanglement-fluctuation relation is evaluated for the ground states of a one-dimensional free-fermion gas and the Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for experimentally measuring entanglement using Stern-Gerlach-type state selectors.
Purification and switching protocols for dissipatively stabilized entangled qubit states
Hein, Sven M.; Aron, Camille; Türeci, Hakan E.
2016-06-01
Pure dephasing processes limit the fidelities achievable in driven-dissipative schemes for stabilization of entangled states of qubits. We propose a scheme which, combined with already existing entangling methods, purifies the desired entangled state by driving out of equilibrium auxiliary dissipative cavity modes coupled to the qubits. We lay out the specifics of our scheme and compute its efficiency in the particular context of two superconducting qubits in a cavity-QED architecture, where the strongly coupled auxiliary modes provided by collective cavity excitations can drive and sustain the qubits in maximally entangled Bell states with fidelities reaching 90% for experimentally accessible parameters.
Multipartite entanglement in four-qubit graph states
Jafarpour, Mojtaba; Assadi, Leila
2016-03-01
We consider a compendium of the non-trivial four-qubit graphs, derive their corresponding quantum states and classify them into equivalent classes. We use Meyer-Wallach measure and its generalizations to study block-partition and global entanglement in these states. We obtain several entanglement quantities for each graph state, which present a comprehensive characterization of the entanglement properties of the latter. As a result, a number of correlations between the graph structure and multipartite entanglement quantities have also been established.
Quantum Secret Sharing with Two-Particle Entangled States
LIU Wei-Tao; LIANG Lin-Mei; LI Cheng-Zu; YUAN Jian-Min
2006-01-01
We present a new protocol for the quantum secret sharing (QSS) task among multiparties with two-particle entangled states. In our scheme, the secret is split among a number of participating partners and the reconstruction requires collaboration of all the authorized partners. Instead of multiparticle Greenberger-Horne-Zeilinger states,only two-particle entangled states are employed in this scheme. By local operations and individual measurements on either of the two entangled particles, each authorized partner obtains a sequence of secret bits shared with other authorized partners. This protocol can be experimentally realized using only linear optical elements and simple entanglement source. It is scalable in practice.
Searching for extremal PPT entangled states
Augusiak, Remigiusz; Kus, Marek; Lewenstein, Maciej
2009-01-01
We formulate a simple operational criterion allowing to judge if a given entangled state with positive partial transpose (PPTES) is extremal in the convex set of all PPTES. The criterion reduces the problem to the question of existence of solutions of a system of linear equations. We apply this criterion to search for extremal PPTES in qubit--ququart systems. We show that the only candidates for extremal PPTES have ranks of the state and its partial transposition (5,5) or (5,6) (equivalently (6,5)). While we show that in the case of (5,5) there do exist extremal states, we conjecture that there are no such states in the case of (5,6), and discuss possible ways to prove this statement.
Wang, He; Zhang, Yu Qing; Liu, Xue Feng; Hu, Yu Pu
2016-06-01
We propose a novel quantum dialogue protocol by using the generalized Bell states and entanglement swapping. In the protocol, a sequence of ordered two-qutrit entangled states acts as quantum information channel for exchanging secret messages directly and simultaneously. Besides, a secret key string is shared between the communicants to overcome information leakage. Different from those previous information leakage-resistant quantum dialogue protocols, the particles, composed of one of each pair of entangled states, are transmitted only one time in the proposed protocol. Security analysis shows that our protocol can overcome information leakage and resist several well-known attacks. Moreover, the efficiency of our scheme is acceptable.
Quantum Dense Coding in Multiparticle Entangled States via Local Measurements
陈建兰; 匡乐满
2004-01-01
We study quantum dense coding between two arbitrarily fixed particles in a (N + 2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted classical information amount through such an entangled quantum channel is usually less than two classical bits. However, the information amount may reach two classical bits of information, and the classical information capacity is independent of the number of the entangled particles under certain conditions. The results offer deeper insight into quantum dense coding via quantum channels of multi-particle entangled states.
Effective thermodynamics of isolated entangled squeezed and coherent states
Seroje, King Karl R; Paraan, Francis N C
2015-01-01
The R\\'enyi entanglement entropy is calculated exactly for mode-partitioned isolated systems such as the two-mode squeezed state and the multi-mode Silbey-Harris polaron ansatz state. Effective thermodynamic descriptions of the correlated partitions are constructed to present quantum information theory concepts in the language of thermodynamics. Boltzmann weights are obtained from the entanglement spectrum by deriving the exact relationship between an effective temperature and the physical entanglement parameters. The partition function of the resulting effective thermal theory can be obtained directly from the single-copy entanglement.
Ota, Y; Ohba, I; Yoshida, N; Mikami, Shuji; Ohba, Ichiro; Ota, Yukihiro; Yoshida, Noriyuki
2006-01-01
Recently, Yu, Brown, and Chuang [Phys. Rev. A {\\bf 71}, 032341 (2005)] investigated the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance (NMR). Their research gave an insight into the role of the entanglement in a liquid-state NMR quantum computer. Moreover, they attempted to reveal the role of mixed-state entanglement in quantum computing. However, they assumed that the Zeeman energy of each nuclear spin which corresponds to a qubit takes a common value for all; there is no chemical shift. In this paper, we research a model with the chemical shifts and analytically derive the physical parameter region where unitary transformed thermal states are entangled, by the positive partial transposition (PPT) criterion with respect to any bipartition. We examine the effect of the chemical shifts on the boundary between the separability and the nonseparability, and find it is negligible.
Entanglement Swapping of Generalized Cat States and Secret Sharing
Karimipour, V; Bahraminasab, A; Karimipour, Vahid; Bagherinezhad, Saber; Bahraminasab, Alireza
2002-01-01
We introduce generalized cat states for d-level systems and obtain concise formulas for their entanglement swapping with generalized Bell states. We then use this to provide both a generalization to the d-level case and a transparent proof of validity for an already proposed protocol of secret sharing based on entanglement swapping
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.
Wang, Meiyu; Yan, Fengli; Xu, Jingzhou
2016-08-01
We show how to concentrate an arbitrary four-photon polarization entangled state into a maximally entangled state based on some quantum nondemolition detectors. The entanglement concentration protocol (ECP) resorts to an ancillary single-photon resource and the conventional projection measurement on photons to assist the concentration, which makes it more economical. Our ECP involves weak cross-Kerr nonlinearities, X homodyne measurement and basic linear-optical elements, which make it feasible in the current experimental technology. Moreover, the ECP considers cyclic utilization to enhance a higher success probability. Thus, our scheme is meaningful in practical applications in quantum communication.
Multiparty Quantum Secret Sharing of Quantum States Using Entanglement States
GUO Ying; HUANG Da-Zu; ZENG Gui-Hua; LEE Moon Ho
2008-01-01
A multi-partite-controlled quantum secret sharing scheme using several non-orthogonal entanglement states is presented with unconditional security.In this scheme,the participants share the secret quantum state by exchanging the secret polarization angles of the disordered travel particles.The security of the secret quantum state is also guaranteed by the non-orthogonal multi-partite-controlled entanglement states,the participants'secret polarizations,and the disorder of the travelling particles.Moreover,the present scheme is secure against the particle-number splitting attack and the intercept-and-resend attack.It may be still secure even if the distributed quantum state is embedded in a not-so-weak coherent-state pulse.
Entanglement of Vector-Polarization States of Photons
Kong, Ling-Jun; Si, Yu; Liu, Rui; Wang, Zhou-Xiang; Tu, Chenghou; Wang, Hui-Tian
2015-01-01
Photons may have homogeneous polarization and may carry quantized orbital angular momentum (OAM). Photon entanglement has been realized in various degrees of freedom such as polarization and OAM. Using a pair of orthogonally polarized states carrying opposite-handedness quantized OAMs could create "quantized" vector polarization states with space-variant polarization structures. It is thus possible to extend the polarization degree of freedom from two dimensional space to indefinite dimensional discrete Hilbert space. We present a class of vector-polarization entangled Bell states, which use the spatial modes of the vector fields with space-variant polarization structure. We propose a scheme of creating the vector-polarization entangled Bell states using a Sagnac interferometer. We also design an analyzer for identifying the vector-polarization entangled Bell states. Such a class of entanglement is important for quantum information science and technology, and fundamental issues of quantum theory, due to its a...
Highly entangled multi-qubit states with simple algebraic structure
Tapiador, J E; Clark, J A; Stepney, S [Department of Computer Science, University of York (United Kingdom); Hernandez-Castro, J C [Department of Computing, University of Portsmouth (United Kingdom)], E-mail: jet@cs.york.ac.uk
2009-10-16
Recent works by Brown et al (2005 J. Phys. A: Math. Gen. 38 1119) and Borras et al (2007 J. Phys. A: Math. Theor. 40 13407) have explored numerical optimization procedures to search for highly entangled multi-qubit states according to some computationally tractable entanglement measure. We present an alternative scheme based upon the idea of searching for states having not only high entanglement but also simple algebraic structure. We report results for 4, 5, 6, 7 and 8 qubits discovered by this approach, showing that many of such states do exist. In particular, we find a maximally entangled 6-qubit state with an algebraic structure simpler than the best results known so far. For the case of 7 qubits, we discover states with high, but not maximum, entanglement and simple structure, as well as other desirable properties. Some preliminary results are shown for the case of 8 qubits.
Generalizations of entanglement based on coherent states and convex sets
2002-01-01
Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativize...
Entangled states of spin and clock oscillators
Polzik, Eugene
2016-05-01
Measurements of one quadrature of an oscillator with precision beyond its vacuum state uncertainty have occupied a central place in quantum physics for decades. We have recently reported the first experimental implementation of such measurement with a magnetic oscillator. However, a much more intriguing goal is to trace an oscillator trajectory with the precision beyond the vacuum state uncertainty in both position and momentum, a feat naively assumed not possible due to the Heisenberg uncertainty principle. We have demonstrated that such measurement is possible if the oscillator is entangled with a quantum reference oscillator with an effective negative mass. The key element is the cancellation of the back action of the measurement on the composite system of two oscillators. Applications include measurements of e.-m. fields, accelleration, force and time with practically unlimited accuracy. In a more general sense, this approach leads to trajectories without quantum uncertainties and to achieving new fundamental bounds on the measurement precision.
Liu Tang-Kun
2007-01-01
By the negative eigenvalues of partial transposition of density matrix, this paper investigates the time evolution of entanglement of the two entangled atoms in the system of two atoms interacting with Schr(o)dinger cat state. The result shows that the two atoms are always in the entanglement state, and the degree of entanglement between the two atoms exhibits ordinary collapses and revivals at 0.2 degree of entanglement, when the light field is large enough. On the other hand, the reinforcement of three different light fields on the degree of entanglement between two atoms is not evident.
Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures
GUO Ying; LIU Dan; ZENG Gui-Hua; ZHAO Xin; Moon Ho Lee; LONG Gui-Lu
2008-01-01
Four-qubit entanglement has been investigated using a recent proposed entanglement measure, multiple entropy measures (MEMS). We have performed optimization for the nine different families of states of four-qubit system. Some extremal entangled states have been found.
Practical single-photon-assisted remote state preparation with non-maximally entanglement
Wang, Dong; Huang, Ai-Jun; Sun, Wen-Yang; Shi, Jia-Dong; Ye, Liu
2016-08-01
Remote state preparation (RSP) and joint remote state preparation (JRSP) protocols for single-photon states are investigated via linear optical elements with partially entangled states. In our scheme, by choosing two-mode instances from a polarizing beam splitter, only the sender in the communication protocol needs to prepare an ancillary single-photon and operate the entanglement preparation process in order to retrieve an arbitrary single-photon state from a photon pair in partially entangled state. In the case of JRSP, i.e., a canonical model of RSP with multi-party, we consider that the information of the desired state is split into many subsets and in prior maintained by spatially separate parties. Specifically, with the assistance of a single-photon state and a three-photon entangled state, it turns out that an arbitrary single-photon state can be jointly and remotely prepared with certain probability, which is characterized by the coefficients of both the employed entangled state and the target state. Remarkably, our protocol is readily to extend to the case for RSP and JRSP of mixed states with the all optical means. Therefore, our protocol is promising for communicating among optics-based multi-node quantum networks.
Entanglement of Formation for Werner States and Isotropic States via Logical Gates
Bertini, Cesarino; Chiara, Maria Luisa Dalla; Leporini, Roberto
To what extent is a logical characterization of entanglement possible? We investigate some correlations that hold between the concept of entanglement of formation for Werner states and for isotropic states and the probabilistic behavior of some quantum logical gates.
Quantum entanglement swapping of two arbitrary biqubit pure states
Xie, ChuanMei; Liu, YiMin; Chen, JianLan; Yin, XiaoFeng; Zhang, ZhanJun
2016-10-01
In this paper, the issue of swapping quantum entanglements in two arbitrary biqubit pure states via a local bipartite entangledstate projective measure in the middle node is studied in depth, especially with regard to quantitative aspects. Attention is mainly focused on the relation between the measure and the final entanglement obtained via swapping. During the study, the entanglement of formation (EoF) is employed as a quantifier to characterize and quantify the entanglements present in all involved states. All concerned EoFs are expressed analytically; thus, the relation between the final entanglement and the measuring state is established. Through concrete analyses, the measure demands for getting a certain amount of a final entanglement are revealed. It is found that a maximally entangled final state can be obtained from any two given initial entangled states via swapping with a certain probability; however, a peculiar measure should be performed. Moreover, some distinct properties are revealed and analyzed. Such a study will be useful in quantum information processes.
Symmetric Telecloning and Entanglement Distribution of Spin Quantum States
WANG Qiong; LI Ji-Xin; ZANG Hao-Sheng
2008-01-01
@@ We propose a physical realization of symmetric telecloning machine for spin quantum states. The concept of area average fidelity is introduced to describe the telecloning quality. It is indicated that for certain input states this quantity may come to an enough high level to satisfy the need of quantum information processing. We also study the properties of entanglement distribution via the spin chain for arbitrary two-qubit entangled pure states as inputs and find that the decay ratio of entanglement for the output states is only determined by the parameters of spin chain and waiting time, independent of the initial input states.
Renormalizing Entanglement Distillation.
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens
2016-01-15
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
Fisher Information and entanglement of non-Gaussian spin states
Strobel, Helmut; Linnemann, Daniel; Zibold, Tilman; Hume, David B; Pezzè, Luca; Smerzi, Augusto; Oberthaler, Markus K
2015-01-01
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement which we confirm by Bayesian phase estimation with sub shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.
Phase-Tuned Entangled State Generation between Distant Spin Qubits
Stockill, R.; Stanley, M. J.; Huthmacher, L.; Clarke, E.; Hugues, M.; Miller, A. J.; Matthiesen, C.; Le Gall, C.; Atatüre, M.
2017-07-01
Quantum entanglement between distant qubits is an important feature of quantum networks. Distribution of entanglement over long distances can be enabled through coherently interfacing qubit pairs via photonic channels. Here, we report the realization of optically generated quantum entanglement between electron spin qubits confined in two distant semiconductor quantum dots. The protocol relies on spin-photon entanglement in the trionic Λ system and quantum erasure of the Raman-photon path information. The measurement of a single Raman photon is used to project the spin qubits into a joint quantum state with an interferometrically stabilized and tunable relative phase. We report an average Bell-state fidelity for |ψ(+)⟩ and |ψ(-)⟩ states of 61.6 ±2.3 % and a record-high entanglement generation rate of 7.3 kHz between distant qubits.
N-Particle Entangled States of Continuum Variables
SONG Tong-Qiang; ZHU Yue-Jin
2003-01-01
We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifestly shown. Finally, we discuss their application.
Backens, Miriam
2017-02-01
L. Lamata et al. use an inductive approach to classify the entangled pure states of four qubits under stochastic local operations and classical communication (SLOCC) [Phys. Rev. A 75, 022318 (2007), 10.1103/PhysRevA.75.022318]. The inductive method yields a priori ten entanglement superclasses, of which they discard three as empty. One of the remaining superclasses is split into two, resulting in eight superclasses of genuine four-qubit entanglement. Here, we show that two of the three discarded superclasses are in fact nonempty and should have been retained. We give explicit expressions for the canonical states of those superclasses, up to SLOCC and qubit permutations. Furthermore, we confirm that the third discarded superclass is indeed empty, yielding a total of ten superclasses of genuine four-qubit entanglement under the inductive classification scheme.
Generation of maximally entangled states of qudits using twin photons
Neves, L; Gómez, J G A; Monken, C H; Saavedra, C; Pádua, S; Neves, Leonardo
2004-01-01
We report an experiment to generate maximally entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D-slits in the arms of the twin fotons define the qudit space. By manipulating the pump beam correctly the twin photons will pass only by symmetrically opposite slits, generating entangled states between these differents paths. Experimental results for qudits with D=4 and D=8 are shown. We demonstrate that the generated states are entangled states.
Feasible Teleportation Schemes with Five-Atom Entangled State
XUE Zheng-Yuan; YI You-Min; CAO Zhuo-Liang
2006-01-01
Teleportation schemes with a five-atom entangled state are investigated. In the teleportation scheme Bell state measurements (BSMs) are difficult for physical realization, so we investigate another strategy using separate measurements instead of BSM based on cavity quantum electrodynamics techniques. The scheme of two-atom entangled state teleportation is a controlled and probabilistic one. For the teleportation of the three-atom entangled state, the scheme is a probabilistic one. The fidelity and the probability of the successful teleportation are also obtained.
Relative entropy as a measure of entanglement for Gaussian states
Lu Huai-Xin; Zhao Bo
2006-01-01
In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres-Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example,the relative entanglement for a two-mode squeezed thermal state has been obtained.
Geometric Entanglement of Symmetric States and the Majorana Representation
Aulbach, Martin; Murao, Mio
2010-01-01
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-b...
Entanglement as a resource to distinguish orthogonal product states.
Zhang, Zhi-Chao; Gao, Fei; Cao, Tian-Qing; Qin, Su-Juan; Wen, Qiao-Yan
2016-07-26
It is known that there are many sets of orthogonal product states which cannot be distinguished perfectly by local operations and classical communication (LOCC). However, these discussions have left the following open question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In m ⊗ n, certain classes of unextendible product bases (UPB) which can be distinguished perfectly using entanglement as a resource, had been presented in 2008. In this paper, we present protocols which use entanglement more efficiently than teleportation to distinguish some classes of orthogonal product states in m ⊗ n, which are not UPB. For the open question, our results offer rather general insight into why entanglement is useful for such tasks, and present a better understanding of the relationship between entanglement and nonlocality.
Quantum frequency up-conversion of continuous variable entangled states
Liu, Wenyuan; Wang, Ning; Li, Zongyang; Li, Yongmin, E-mail: yongmin@sxu.edu.cn [State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006 (China)
2015-12-07
We demonstrate experimentally quantum frequency up-conversion of a continuous variable entangled optical field via sum-frequency-generation process. The two-color entangled state initially entangled at 806 and 1518 nm with an amplitude quadrature difference squeezing of 3.2 dB and phase quadrature sum squeezing of 3.1 dB is converted to a new entangled state at 530 and 1518 nm with the amplitude quadrature difference squeezing of 1.7 dB and phase quadrature sum squeezing of 1.8 dB. Our implementation enables the observation of entanglement between two light fields spanning approximately 1.5 octaves in optical frequency. The presented scheme is robust to the excess amplitude and phase noises of the pump field, making it a practical building block for quantum information processing and communication networks.
Detecting Multiparticle Entanglement of Dicke States
Lücke, Bernd; Peise, Jan; Vitagliano, Giuseppe
2014-01-01
Recent experiments demonstrate the production of many thousands of neutral atoms entangled in their spin degrees of freedom. We present a criterion for estimating the amount of entanglement based on a measurement of the global spin. It outperforms previous criteria and applies to a wider class...
Fast entanglement detection for unknown states of two spatial qutrits
Lima, G; Vargas, A; Vianna, R O; Saavedra, C
2010-01-01
We investigate the practicality of the method proposed by Maciel et al. [Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial qutrits (3-dimensional quantum systems), which are encoded in the discrete transverse momentum of single photons transmitted through a multi-slit aperture. The method is based on the acquisition of partial information of the quantum state through projective measurements, and a data processing analysis done with semi-definite programs. This analysis relies on generating gradually an optimal entanglement witness operator, and numerical investigations have shown that it allows for the entanglement detection of unknown states with a cost much lower than full state tomography.
High-Fidelity Entangled Bell States via Shortcuts to Adiabaticity
Paul, Koushik
2016-01-01
We present a couple of protocols based on shortcut to adiabaticity techniques for rapid generation of robust entangled Bell states in a system of two two-state systems. Our protocols rely on the so-called transitionless quantum driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD and LRI methods result in high fidelity in population transfer.Our study shows that it is possible to prepare an entangled state in infinitely short time without losing robustness and efficiency.
Dissipative production of a maximally entangled steady state
Lin, Y; Reiter, F; Tan, T R; Bowler, R; S\\orensen, A S; Leibfried, D; Wineland, D J
2013-01-01
Entangled states are a key resource in fundamental quantum physics, quantum cryp-tography, and quantum computation [1].To date, controlled unitary interactions applied to a quantum system, so-called "quantum gates", have been the most widely used method to deterministically create entanglement [2]. These processes require high-fidelity state preparation as well as minimizing the decoherence that inevitably arises from coupling between the system and the environment and imperfect control of the system parameters. Here, on the contrary, we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion qubits independent of their initial state. While previous works along this line involved the application of sequences of multiple time-dependent gates [3] or generated entanglement of atomic ensembles dissipatively but relied on a measurement record for steady-state entanglement [4], we implement the process in a continuous time-indepen...
Entanglement of the orbital angular momentum states of photons.
Mair, A; Vaziri, A; Weihs, G; Zeilinger, A
2001-07-19
Entangled quantum states are not separable, regardless of the spatial separation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum non-locality. An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement. Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons. Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum. As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography.
Entanglement entropy scaling in solid-state spin arrays via capacitance measurements
Banchi, Leonardo; Bayat, Abolfazl; Bose, Sougato
2016-12-01
Solid-state spin arrays are being engineered in varied systems, including gated coupled quantum dots and interacting dopants in semiconductor structures. Beyond quantum computation, these arrays are useful integrated analog simulators for many-body models. As entanglement between individual spins is extremely short ranged in these models, one has to measure the entanglement entropy of a block in order to truly verify their many-body entangled nature. Remarkably, the characteristic scaling of entanglement entropy, predicted by conformal field theory, has yet to be measured. Here, we show that with as few as two replicas of a spin array, and capacitive double-dot singlet-triplet measurements on neighboring spin pairs, the above scaling of the entanglement entropy can be verified. This opens up the controlled simulation of quantum field theories, as we exemplify with uniform chains and Kondo-type impurity models, in engineered solid-state systems. Our procedure remains effective even in the presence of typical imperfections of realistic quantum devices and can be used for thermometry, and to bound entanglement and discord in mixed many-body states.
Teleportation of a Kind of Three-Mode Entangled States of Continuous Variables
无
2005-01-01
A quantum teleportation scheme to teleport a kind of tripartite entangled states of continuous variables by using a quantum channel composed of three bipartite entangled states is proposed. The joint Bell measurement is feasible because the bipartite entangled states are complete and the squeezed state has a natural representation in the entangled state basis. The calculation is greatly simplified by using the Schmidt decomposition of the entangled states.
Protecting entangled states of two ions by engineering reservoir
Xue Dong; Zou Jian; Yang Linguang; Li Jungang; Shao Bin, E-mail: zoujian@bit.edu.cn [Department of Physics, School of Science, Beijing Institute of Technology, Beijing 100081 (China)
2011-09-14
We present a proposal for realizing local decoherence-free evolution of given entangled states of two two-level (TL) ions. For two TL ions coupled to a single heavily damped cavity, we can use an engineering reservoir scheme to obtain a decoherence-free subspace which can be nonadiabatically controlled by the system and reservoir parameters. Then the local decoherence-free evolution of the entangled states is achieved. And we also discuss the relation between the geometric phases and the entanglement of the two ions under the nonadiabatic coherent evolution.
Probabilistic Teleportation of a Four-Particle Entangled W State
ZHAN You-Bang; FU Hao
2005-01-01
In this paper, two schemes for teleporting an unknown four-particle entangled W state is proposed. In the first scheme, two partial entangled four-particle states are used as quantum channels, while in the second scheme,four non-maximally entangled particle pairs are considered as quantum channels. It is shown that the teleportation can be successfully realized with certain probability, for both schemes, if a receiver adopts some appropriate unitary transformations. It is also shown that the successful probabilities of these two schemes are different.
Preparation of entangled states through Hilbert space engineering
Lin, Y; Reiter, F; Tan, T R; Bowler, R; Wan, Y; Keith, A; Knill, E; Glancy, S; Coakley, K; Sørensen, A S; Leibfried, D; Wineland, D J
2016-01-01
Entangled states are a crucial resource for quantum-based technologies such as quantum computers and quantum communication systems (1,2). Exploring new methods for entanglement generation is important for diversifying and eventually improving current approaches. Here, we create entanglement in atomic ions by applying laser fields to constrain the evolution to a restricted number of states, in an approach that has become known as "quantum Zeno dynamics" (3-5). With two trapped $^9\\rm{Be}^+$ ions, we obtain Bell state fidelities up to $0.990^{+2}_{-5}$, with three ions, a W-state (6) fidelity of $0.910^{+4}_{-7}$ is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure is relatively insensitive to certain imperfections such as fluctuations in laser intensity, laser frequency, and ion-motion frequencies.
Fingerprints of entangled states in reactions with rare isotopes
Bertulani, C A
2003-01-01
We study the presence of entangled states of nucleon pairs from nuclear decays and in reactions with exotic nuclei, e.g., 11Li, or 6He. It is shown that the fingerprints of entangled states in these subsystems are visible in correlation measurements and can be accessed with present experimental techniques. This shows that not only atomic and optical systems, but also nuclear systems serve as important tools to obtain dichotomic outcomes for tests of the Einstein-Podolsky-Rosen paradox.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
FANHong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two panicles' relative coordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantum point-mass pendulum. The Hamiltonian displays the correct Schroedlnger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation are derived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
FAN Hong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two particles'relativecoordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantumpoint-mass pendulum. The Hamiltonian displays the correct Schrodinger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation arederived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Multipartite entanglement in neutrino oscillations
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2009-06-01
Particle mixing is related to multi-mode entanglement of single-particle states The occupation number of both flavor eigenstates and mass eigenstates can be used to define a multiqubit space. In such a framework, flavor neutrino states can be interpreted as multipartite mode-entangled states. By using two different entanglement measures, we analyze the behavior of multipartite entanglement in the phenomenon of neutrino oscillations.
A Note on Entanglement Entropy, Coherent States and Gravity
Varadarajan, Madhavan
2016-01-01
The entanglement entropy of a free quantum field in a coherent state is independent of its stress energy content. We use this result to highlight the fact that while the Einstein equations for first order variations about a locally maximally symmetric vacuum state of geometry and quantum fields seem to follow from Jacobson's principle of maximal vacuum entanglement entropy, their possible derivation from this principle for the physically relevant case of finite but small variations remains an open issue. We also apply this result to the context of Bianchi's identification, independent of unknown Planck scale physics, of the first order variation of Bekenstein Hawking area with that of vacuum entanglement entropy. We argue that under certain technical assumptions this identification seems not to be extendible to the context of finite but small variations to coherent states. Our particular method of estimation of entanglement entropy variation reveals the existence of certain contributions over and above those ...
Arbitrated quantum signature schemes without using entangled states
Zou, Xiangfu
2010-01-01
A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or document. For signing quantum messages, some arbitrated quantum signature schemes have being proposed. However, in the existing literature, arbitrated quantum signature schemes depend on entanglement. In this paper, we present two arbitrated quantum signature schemes without utilizing entangled states in the signing phase and the verifying phase. The first proposed scheme can preserve the merits in the existing schemes. Then, we point out, in this scheme and the prior schemes, there exists a problem that Bob can repudiate the integrality of the signatures. To conquer this problem, we construct another arbitrated quantum signature scheme without using quantum entangled states but using a public board. The new scheme has three advantages: it does not utilize entangled states while it can preserve all merits in the existing schemes; the integrality of the signature can avoid being disavowed by the receiver; an...
Robust entangled qutrit states in atmospheric turbulence
Brunner, T
2013-06-01
Full Text Available ) = |ψ〉〈ψ|, where |ψ〉 is given in (1), using the coefficients defined in (3). Although, we assume that the initial state (1) is a pure state, the scintillation process causes it to become mixed during propagation, which necessitates a density matrix... turbulence (a) and weak turbulence (b). To find the most robust states we optimize the tangle at a particular point t = t0, for the general initial pure state, using the parameterization from (3). This optimization process is similarly to [8]. From...
Teleportation with Tripartite Entangled State via Thermal Cavity
XUE Zheng-Yuan; YI You-Min; CAO Zhuo-Liang
2006-01-01
Teleportation schemes with a tripartite entangled state in cavity QED are investigated. The schemes do not need Bell state measurements and the successful probabilities reach optimality. In addition, the schemes are insensitive to both the cavity decay and the thermal field. We first consider two teleportation schemes via a tripartite GHZ state.The first one is a controlled one for an unknown single-qubit state. The second scheme is teleportation of unknown two-atom entangled state. Then we consider teleporting of single-qubit arbitrary state via a tripartite W state.
High-Frequency Einstein-Podolsky-Rosen Entanglement via Atomic Memory Effects in Four-Wave Mixing
ZHANG Xue-Hua; HU Xiang-Ming; KONG Ling-Feng; ZHANG Xiu
2010-01-01
@@ Atomic memory effects occur when the atomic relaxation times are comparable to or much longer than the cavity relaxation times.We show that by using the memory effects,it is possible to obtain high-frequency Einstein-Podolsky-Rosen entanglement between a pair of Stokes and anti-Stokes fields in a four-wave mixing system.The physical origin is traced to the dynamical Stark splittings of dressed states due to the parametrically amplified fields.This mechanism provides an alternative and efficient way for sideband entanglement.
Entangled-state cycles from conditional quantum evolution
Gu, M; Parkins, S
2006-01-01
A system of cascaded qubits interacting via the oneway exchange of photons is studied. While for general operating conditions the system evolves to a superposition of Bell states (a dark state) in the long-time limit, under a particular resonance condition no steady state is reached within a finite time. We analyze the conditional quantum evolution (quantum trajectories) to characterize the asymptotic behavior under this resonance condition. A distinct bimodality is observed: for perfect qubit coupling, the system either evolves to a maximally entangled Bell state without emitting photons (the dark state), or executes a sustained entangled-state cycle - random switching between a pair of Bell states while emitting a continuous photon stream; for imperfect coupling, two entangled-state cycles coexist, between which a random selection is made from one quantum trajectory to another.
Amplification of maximally-path-entangled number states
Agarwal, G. S.; Chaturvedi, S.; Rai, Amit
2010-04-01
We examine the behavior of a non-Gaussian state like the maximally path-entangled number state commonly known as a N00N state under phase-insensitive amplification. We derive an analytical result for the density matrix of the N00N state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the N00N state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that N00N states are more robust than their Gaussian counterparts.
Multi-mode entangled states represented as Grassmannian polynomials
Maleki, Y.
2016-09-01
We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map the Hilbert space of the finite-dimensional multi-mode states to the space of some Grassmannian polynomial functions. These Grassmannian polynomials form a well-defined space in the framework of Grassmann variables; namely Grassmannian representative space. Therefore, a quantum state can be uniquely defined and determined by an element of Grassmannian representative space. Furthermore, the Grassmannian representatives of some maximally entangled states are considered, and it is shown that there is a tight connection between the entanglement of the states and their Grassmannian representatives.
General monogamy relations of quantum entanglement for multiqubit W-class states
Zhu, Xue-Na; Fei, Shao-Ming
2017-02-01
Entanglement monogamy is a fundamental property of multipartite entangled states. We investigate the monogamy relations for multiqubit generalized W-class states. Analytical monogamy inequalities are obtained for the concurrence of assistance, the entanglement of formation, and the entanglement of assistance.
Bounds for entanglement of formation of two mode squeezed thermal states
Chen, X Y; Chen, Xiao-Yu; Qiu, Pei-liang
2003-01-01
The upper and lower bounds of entanglement of formation are given for two mode squeezed thermal state. The bounds are compared with other entanglement measure or bounds. The entanglement distillation and the relative entropy of entanglement of infinitive squeezed state are obtained at the postulation of hashing inequality.
Approximating local observables on projected entangled pair states
Schwarz, M.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the computational hardness of contracting projected entangled pair states in two- and higher-dimensional systems is often seen as a significant obstacle when devising higher-dimensional variants of the density-matrix renormalization group method. In this work, we show that for those projected entangled pair states that are expected to provide good approximations of such ground states of local Hamiltonians, one can compute local expectation values in quasipolynomial time. We therefore provide a complexity-theoretic justification of why state-of-the-art numerical tools work so well in practice. We finally turn to the computation of local expectation values on quantum computers, providing a meaningful application for a small-scale quantum computer.
Test of Nonlocality with an Atom-Field Entangled State
ZHENG Shi-Biao
2002-01-01
We propose a scheme for the test of nonlocality with atom-field entanglement. An atom is sent through a cavity filled with a coherent field with a small amplitude. The dispersive interaction leads to atom-field entanglement.Then the field is driven by a classical current. The Bell inequality can be tested by the joint measurement of the parity of the field and the atomic state.
Deterministic generation of entangled coherent states for two atomic samples
Lu Dao-Ming; Zheng Shi-Biao
2009-01-01
This paper proposes an efficient scheme for deterministic generation of entangled coherent states for two atomic samples. In the scheme two collections of atoms are trapped in an optical cavity and driven by a classical field. Under certain conditions the two atomic samples evolve from an coherent state to an entangled coherent state. During the interaction the cavity mode is always in the vacuum state and the atoms have no probability of being populated in the excited state. Thus, the scheme is insensitive to both the cavity decay and atomic spontaneous emission.
Preparation of two and four-atom entangled states
无
2000-01-01
A scheme for preparing two and four-atom entangled states is presented. It is based on atom-cavity-field interactions. Firatly, the cav ity is prepared in the superposition of the number states through the atom under going a two-photon transition, the secondly, the two or four identical two-lev el atoms, which are all initially in their ground states, are sent through the c avity sequentially and can make resonant single-photon transition in the cavity . Then atomic entangled states are created and the cavity is left in the vacuum state.
Mixed State Geometric Phase from Thomas Rotations
Lévai, Peter
2003-01-01
It is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by $2\\times 2$ density matrices is just the path ordered product of Thomas rotations. These rotations are invariant under hyperbolic translations inside the Bloch sphere that can be regarded as the Poincar\\'e ball model of hyperbolic geometry. A general expression for the mixed state geometric phase for an {\\it arbitrary} geodesic triangle in terms of the Bures fidelities is derived. The formula gives back the solid angle result well-known from studies of the pure state geometric phase. It is also shown that this mixed state anholonomy can be reinterpreted as the pure state non-Abelian anholonomy of entangled states living in a suitable restriction of the quaternionic Hopf bundle. In this picture Uhlmann's parallel transport is just Pancharatnam transport of quaternionic spinors.
Entanglement and Majorana edge states in the Kitaev model
Mandal, Saptarshi; Maiti, Moitri; Varma, Vipin Kerala
2016-07-01
We investigate the von Neumann entanglement entropy and Schmidt gap in the vortex-free ground state of the Kitaev model on the honeycomb lattice for square/rectangular and cylindrical subsystems. We find that, for both the subsystems, the free-fermionic contribution to the entanglement entropy SE exhibits signatures of the phase transitions between the gapless and gapped phases. However, within the gapless phase, we find that SE does not show an expected monotonic behavior as a function of the coupling Jz between the suitably defined one-dimensional chains for either geometry; moreover, the system generically reaches a point of minimum entanglement within the gapless phase before the entanglement saturates or increases again until the gapped phase is reached. This may be attributed to the onset of gapless modes in the bulk spectrum and the competition between the correlation functions along various bonds. In the gapped phase, on the other hand, SE always monotonically varies with Jz independent of the subregion size or shape. Finally, further confirming the Li-Haldane conjecture, we find that the Schmidt gap Δ defined from the entanglement spectrum also signals the topological transitions but only if there are corresponding zero-energy Majorana edge states that simultaneously appear or disappear across the transitions. We analytically corroborate some of our results on entanglement entropy, the Schmidt gap, and the bulk-edge correspondence using perturbation theory.
Left-right entanglement entropy of boundary states
Zayas, Leopoldo A. Pando [Michigan Center for Theoretical Physics,Randall Laboratory of Physics, The University of Michigan,Ann Arbor, MI 48109-1120 (United States); Quiroz, Norma [Facultad de Ciencias, Universidad de Colima,Bernal Díaz del Castillo 340, Col. Villas San Sebastián,Colima 28045 (Mexico)
2015-01-21
We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.
Left-Right Entanglement Entropy of Boundary States
Zayas, Leopoldo A Pando
2014-01-01
We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal gas of photons. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.
Multi-state Quantum Teleportation via One Entanglement State
GUO Ying; ZENG Gui-Hua; Moon Ho Lee
2008-01-01
A multi-sender-controlled quantum teleportation scheme is proposed to teleport several secret quan-tum states from different senders to a distance receiver based on only one Einstein-Podolsky-Rosen (EPR) pair with controlled-NOT (CNOT) gates. In the present scheme, several secret single-qubit quantum states are encoded into a multi-qubit entangled quantum state. Two communication modes, i.e., the detecting mode and the message mode, are employed so that the eavesdropping can be detected easily and the teleported message may be recovered efficiently. It has an advantage over teleporting several different quantum states for one scheme run with more efficiency than the previous quantum teleportation schemes.
Entanglement Equivalence of $N$-qubit Symmetric States
Mathonet, P; Godefroid, M; Lamata, L; Solano, E; Bastin, T
2009-01-01
We study the interconversion of multipartite symmetric $N$-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or GHZ entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric $N$-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.
Perfect Entanglement Teleportation via Two Parallel W State Channels
WANG Mei-Yu; YAN Feng-Li
2011-01-01
We present a scheme for perfectly teleporting a two-qubit entangled state via two parallel W state channels. The scheme consists of a positive operator valued measurement (POVM), classical communication and the corresponding local unitary operation. How to realize the POVM using unitary operation and projective measurement is explicitly designed.%@@ We present a scheme for perfectly teleporting a two-qubit entangled state via two parallel W state channels.The scheme consists of a positive operator valued measurement (POVM), classical communication and the corre- sponding local unitary operation.How to realize the POVM using unitary operation and projective measurement is explicitly designed.
Entanglement of two ground state neutral atoms using Rydberg blockade
Miroshnychenko, Yevhen; Browaeys, Antoine; Evellin, Charles
2011-01-01
We report on our recent progress in trapping and manipulation of internal states of single neutral rubidium atoms in optical tweezers. We demonstrate the creation of an entangled state between two ground state atoms trapped in separate tweezers using the effect of Rydberg blockade. The quality of...
Thermodynamical state space measure and typical entanglement of pure Gaussian states
Serafini, A; Plenio, M B; Dahlsten, Oscar C.O.; Plenio, Martin B.; Serafini, Alessio
2006-01-01
We introduce a 'microcanonical' measure (complying with the "general canonical principle") over the second moments of pure Gaussian states under an energy constraint. We apply the defined measure to investigate the statistical properties of the bipartite entanglement of pure Gaussian states. Under the proposed measure, the distribution of the entanglement concentrates around a finite value at the thermodynamical limit and, in general, the typical entanglement of Gaussian states with maximal energy E is not close to the maximum allowed by E.
Probabilistic Remote Preparation of a Tripartite High-Dimensional Equatorial Entangled State
SHI Jin; ZHAN You-Bang
2009-01-01
We present a scheme for probabilistic remote preparation of a tripartite qutrit entangled state with a partial tripartite qutrit entangled state and a partial bipartite qutrit entangled state as the quantum channel.It is found that a bipartite qutrit orthogonal projective measurement, an auxiliary qutrit particle, and the corresponding unitary transformation are required.A scheme for probabilistic remote preparation of a tripartite qudit equatorial entangled state by using a partial tripartite qudit entangled state and a partial bipartite qudit entangled state as the quantum channel is also proposed.We calculate the successful total probability and the total classical communication cost required in the RSP process, respectively.
Broadcasting of Entanglement in Three-Particle Greenberger-Horne-Zeilinger State via Quantum Copying
TONG Zhao-Yang; KUANG Le-Man
2000-01-01
We introduce entanglement measures to describe entanglement in a three-particle system and apply it to studying broadcasting of entanglement in the three-particle Greenberger-Horne-Zeilinger (GHZ) state. The results show that the entanglement of the three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement.
Quantum Entanglement of Locally Excited States in Maxwell Theory
Nozaki, Masahiro
2016-01-01
In 4 dimensional Maxwell gauge theory, we study the changes of (Renyi) entangle-ment entropy which are defined by subtracting the entropy for the ground state from the one for the locally excited states generated by acting with the gauge invariant local operators on the state. The changes for the operators which we consider in this paper reflect the electric-magnetic duality. The late-time value of changes can be interpreted in terms of electromagnetic quasi-particles. When the operator constructed of both electric and magnetic fields acts on the ground state, it shows that the operator acts on the late-time structure of quantum entanglement differently from free scalar fields.
Teleportation of a multiqubit state by an entangled qudit channel
郑亦庄; 顾永建; 吴桂初; 郭光灿
2003-01-01
We investigate the problem of teleportation of an M-qubit state by using an entangled qudit pair as a quantum channe; and show that the teleportation of a multiparticle state can correspond to the teleportation of a multidimensional state.We also introduce a quantum-state converter composed of beamspliter arrays,on /off -detectors and coross-Kerr couplers and demonstrate that the stte concersion from an M-qubit to an N-dimensional qudit and vice versa can be implemented with this converter,where N=2M,Based on this ,an experimentallu feasible for the teleportation of an M-qubit via an entangl;ed N-level qudit pair channel is proposed.
Phase-sensitive cascaded four-wave mixing processes for generating continuous-variable entanglement.
Wang, Li; Jing, Jietai
2017-03-20
Quantum entanglement shared by different parties enhances their capabilities to communicate, which is the core content of continuous-variable quantum optics and quantum information science. Here, we study an experimentally feasible scheme for generating quantum entanglement of bipartite and tripartite cases based on phase-sensitive cascaded four-wave mixing processes in rubidium vapor. Quantum entanglement of bipartite and tripartite cases in our system, which can be manipulated by the phases and the intensity gains of the input beams, is predicted. We also find a sufficient optimal single-condition criterion to give a valid description for genuine tripartite quantum entanglement in our system. The sufficient optimal single-condition criterion is convenient and can be extended to genuine multipartite entanglement.
q-Deformed Entangled States Representations and Some Applications
XU Ye-Jun; SONG Jun; YUAN Hong-Chun; LIU Qiu-Yu
2011-01-01
The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator.In similar way, by virtue of the technique of integration within an ordered product (IWOP) of operators, the new completeness and orthogonality relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained.Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited.Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.
The beam splitter as a state and entanglement detector
Berlin, G
2003-01-01
In this article we propose a very simple scheme for detecting the state and the degree of entanglement of two modes of radiation using a beam splitter. We find that using this device we can tell whether the state coming out of a certain apparatus is maximally entangled, by measuring the intensity of the radiation of one of the modes. This result is independent of the transmittivity of the beam splitter. In some cases it is also possible to determine the state exactly, by measuring the dispersion of one of the modes.
Ye, Tian-Yu
2016-09-01
Recently, Liu et al. proposed a two-party quantum private comparison (QPC) protocol using entanglement swapping of Bell entangled state (Commun. Theor. Phys. 57 (2012) 583). Subsequently Liu et al. pointed out that in Liu et al.'s protocol, the TP can extract the two users' secret inputs without being detected by launching the Bell-basis measurement attack, and suggested the corresponding improvement to mend this loophole (Commun. Theor. Phys. 62 (2014) 210). In this paper, we first point out the information leakage problem toward TP existing in both of the above two protocols, and then suggest the corresponding improvement by using the one-way hash function to encrypt the two users' secret inputs. We further put forward the three-party QPC protocol also based on entanglement swapping of Bell entangled state, and then validate its output correctness and its security in detail. Finally, we generalize the three-party QPC protocol into the multi-party case, which can accomplish arbitrary pair's comparison of equality among K users within one execution. Supported by the National Natural Science Foundation of China under Grant No. 61402407
Wang, Zhen; Li, Heng-Mei; Yuan, Hong-Chun
2016-10-01
We theoretically introduce a kind of non-Gaussian entangled states, i.e., photon-subtracted two-mode squeezed coherent states (PSTMSCS), by successively subtracting photons from each mode of the two-mode squeezed coherent states. The normalization factor which is related to bivariate Hermite polynomials is obtained by virtue of the two-mode squeezing operator in entangled-states representation. The sub-Poissonian photon statistics, antibunching effects, and partial negative Wigner function, respectively, are observed numerically, which fully reflect the nonclassicality of the resultant states. Finally, employing the SV criteria and the EPR correlation, respectively, the entangled property of PSTMSCS is analyzed. It is shown that the photon subtraction operation can effectively enhance the inseparability between the two modes.
Preparing projected entangled pair states on a quantum computer.
Schwarz, Martin; Temme, Kristan; Verstraete, Frank
2012-03-16
We present a quantum algorithm to prepare injective projected entangled pair states (PEPS) on a quantum computer, a class of open tensor networks representing quantum states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.
Teleportation of atomic entangled states with a thermal cavity
Zheng Xiao-Juan; Fang Mao-Fa; Cai Jian-Wu; Liao Xiang-Ping
2006-01-01
We propose a most simple and experimentally feasible scheme for teleporting unknown atomic entangled states in driven cavity quantum electrodynamics (QED). In our scheme, the joint Bell-state measurement (BSM) is not required,and the successful probability can reach 1.0. Furthermore, the scheme is insensitive to the cavity decay and the thermal field.
Entanglement properties in (1/2,1) mixed-spin Heisenberg systems
Sun, Z; Hu, A Z; Li, Y Q; Sun, Zhe; Wang, XiaoGuang; Hu, AnZi; Li, You-Quan
2005-01-01
By using the concept of negativity, we investigate entanglement in (1/2,1) mixed-spin Heisenberg systems. We obtain the analytical results of entanglement in small isotropic Heisenberg clusters with only nearest-neighbor (NN) interactions up to four spins and in the four-spin Heisenberg model with both NN and next-nearest-neighbor (NNN) interactions. For more spins, we numerically study effects of temperature, magnetic fields, and NNN interactions on entanglement. We study in detail the threshold value of the temperature, after which the negativity vanishes.
Stability of Pairwise Entanglement in Decoherence Environment
蔡建明
2004-01-01
@@ Consider the dynamics of a bipartite entangled system in the decoherence environment, we investigate the stability of pairwise entanglement under decoherence.We find that with the same initial entanglement, the lifetime of entanglement in pure states and some mixed states is the longest.We call these special entangled states as Decoherence Path States (DPS).Besides, we present simple analytic evolution equations of the entanglement in these states.The lifetimes can also be obtained easily.Furthermore, we also study the stability of the nearest neighbor entanglement in the ground state of an antiferromagnetic spin-1/2 ring.Coincidentally, the conclusion is that it is as stable as Decoherence Path States.Thus the nearest neighbor entanglement in the ground state is not maximized but it is the most stable.This interesting result links the energy and entanglement in a spin system from a new point of view.
Thermal entanglement in a mixed-spin Heisenberg XXZ model under a nonuniform external magnetic field
无
2009-01-01
The thermal entanglement in (1/2,1) mixed-spin Heisenberg XXZ model is investigated under an external nonuniform magnetic field. In the uniform magnetic field system,the critical magnetic field Bc and critical temperature Tc are increased by increasing the anisotropic parameter k. The degree of magnetic field b plays an important role in improving the critical temperature and enlarging the region of entan-glement in the nonuniform magnetic field system.
Entanglement structure of non-equilibrium steady states
Mahajan, Raghu; Mumford, Sam; Tubman, Norm; Swingle, Brian
2016-01-01
We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach is based on the structure of entanglement in the NESS. With reasonable physical assumptions, we show that a NESS close to local equilibrium is lightly entangled and can be represented via a computationally efficient tensor network. We further argue that the NESS may be found by dynamically evolving the system within a manifold of appropriate low entanglement states. A physically realistic law of dynamical evolution is Markovian open system dynamics, or the Lindblad equation. We explore this approach in a well-studied free fermion model where comparisons with the literature are possible. We study both electrical and thermal currents with and without disorder, and compute entropic quantities such as mutual information and conditional mutual information. We conclude with a di...
Entangled States in Quantum Cosmology and the Interpretation of Λ
Orlando Luongo
2011-02-01
Full Text Available The cosmological constant Λ can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e., Ωm and Ωk, which assign the cosmic dynamics. In particular, we consider a cosmological model where two regions, corresponding to two correlated eras, are involved; the present universe description would be, in this way, given by a density matrix ˆρ, corresponding to an entangled final state. Starting from this assumption, it is possible to infer some considerations on the cosmic thermodynamics by evaluating the Von Neumann entropy. The correlation between different regions by the entanglement phenomenon results in the existence of Λ (in particular ΩΛ which could be interpreted in the framework of the recent astrophysical observations. As a byproduct, this approach could provide a natural way to solve the so called coincidence problem.
The "Quantum Mousetrap": Entangled States and Gravitational Waves
Tamburini, Fabrizio; Ungarelli, Carlo
2008-01-01
We propose a "thought technique" for detecting Gravitational Waves using Einstein-Podolski-Rosen photon Entangled States. GWs decohere the entangled photon pairs, introduce a relative rotation and de-synchronize Alice and Bob's reference frames thus reducing the measured non-locality of correlated quanta described by Bell's inequalities. Gravitational Waves, distorting quantum encryption key statistics away from a pure white noise, act then as shadow eavesdroppers. The deviation from the intrinsic white-noise randomness of a Quantum Key Distribution process can reveal the presence of a gravitational wave by analyzing the emerging color distortions in the key. Photon entangled states provide the key advantage of revealing the polarization rotation introduced by GWs without the need of previously fixed reference frames
Properties of the Measurement Phase Operator in Dual-Mode Entangle Coherent States
HOU Shen-Yong; YANG Kuo
2011-01-01
@@ A class of measurement phase operators of dual-mode is defined and their properties in a class of entangle coherent states are investigated.Numerical results indicate that the entangle coherent states display some non-classical squeezed effects.%A class of measurement phase operators of dual-mode is defined and their properties in a class of entangle coherent states are investigated. Numerical results indicate that the entangle coherent states display some non-classical squeezed effects.
Cardoso B., W.; Almeida G. de, N.
2008-07-01
We propose a scheme to partially teleport an unknown entangled atomic state. A high-Q cavity, supporting one mode of a weak coherent state, is needed to accomplish this process. By partial teleportation we mean that teleportation will occur by changing one of the partners of the entangled state to be teleported. The entangled state to be teleported is composed by one pair of particles, we called this surprising characteristic of maintaining the entanglement, even when one of the particle of the entangled pair being teleported is changed, of divorce of entangled states.
W. B. Cardosol; N. G. de Almeida
2008-01-01
We propose a scheme to partially teleport an unknown entangled atomic state. A high-Q cavity, supporting one mode of a weak coherent state, is needed to accomplish this process. By partial teleportation we mean that teleportation will occur by changing one of the partners of the entangled state to be teleported. The entangled state to be teleported is composed by one pair of particles, we called this surprising characteristic of maintaining the entanglement, even when one of the particle of the entangled pair being teleported is changed, of divorce of entangled states.
Entanglement in a solid-state spin ensemble.
Simmons, Stephanie; Brown, Richard M; Riemann, Helge; Abrosimov, Nikolai V; Becker, Peter; Pohl, Hans-Joachim; Thewalt, Mike L W; Itoh, Kohei M; Morton, John J L
2011-02-03
Entanglement is the quintessential quantum phenomenon. It is a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing and the strongest forms of quantum cryptography. Spin ensembles, such as those used in liquid-state nuclear magnetic resonance, have been important for the development of quantum control methods. However, these demonstrations contain no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered, phosphorus-doped silicon. We combined high-field (3.4 T), low-temperature (2.9 K) electron spin resonance with hyperpolarization of the (31)P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% relative to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, on 10(10) spin pairs; this fulfils one of the essential requirements for a silicon-based quantum information processor.
无
2007-01-01
We present two schemes for preparing remotely a three-particle entangled state by two different quantum channels. In the first scheme, two partial three-particle entangled states are used as the quantum channels, while in the second scheme, three two-particle non-maximally entangled states are employed as the quantum channels. It is shown that the remote state preparation can be successfully realized with certain probability, for both two schemes, if a sender performs some projective measurements and a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.
Optical Generation of Single- or Two-Mode Excited Entangled Coherent States
REN Zhen-Zhong; JING Hui; ZHANG Xian-Zhou
2008-01-01
With nonlinear Mach-Zehnder interferometer (NLMZI) and a type-Ⅰ beta-barium borate (BBO) crystal, we optically generate single-mode excited entangled coherent states. This scheme can be easily generalized to generate two-mode excited entangled coherent states. We simply analyse different influences of single- and two-mode photon excitations on entangled coherent states.
Maximal entanglement of squeezed vacuum states via swapping with number-phase measurement
Kitagawa, A; Kitagawa, Akira; Yamamoto, Katsuji
2002-01-01
We propose a method to realize entanglement via swapping from a pair of squeezed vacuum states by performing number sum and phase difference measurements. The resultant states are maximally entangled by adjusting the two squeezing parameters to the same value. We then describe a teleportation protocol by using the entangled states prepared in this way.
Non-locality of Entangled Coherent States and Its Evolution in a Thermal Reservoir
GONG Ren-Shan
2005-01-01
Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for nonlocality of entangled states, we present a perturbative calculation determining non-locality of evolving entangled states.Furthermore, by means of the perturbative calculation, the non-locality and its evolution of two kinds of entangled coherent states in a thermal reservoir are discussed.
Quantum Correlations in Mixed-State Metrology
Kavan Modi
2011-12-01
Full Text Available We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated single-qubit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits and time (number of gates requirements, we introduce mixedness as a key constraint of the experiment. We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives sqrt[N] enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.
Generating and probing entangled states for optical atomic clocks
Braverman, Boris; Kawasaki, Akio; Vuletic, Vladan
2016-05-01
The precision of quantum measurements is inherently limited by projection noise caused by the measurement process itself. Spin squeezing and more complex forms of entanglement have been proposed as ways of surpassing this limitation. In our system, a high-finesse asymmetric micromirror-based optical cavity can mediate the atom-atom interaction necessary for generating entanglement in an 171 Yb optical lattice clock. I will discuss approaches for creating, characterizing, and optimally utilizing these nonclassical states for precision measurement, as well as recent progress toward their realization. This research is supported by DARPA QuASAR, NSF, and NSERC.
Standard forms and entanglement engineering of multimode Gaussian states under local operations
Serafini, Alessio [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, SW7 2PG (United Kingdom); Adesso, Gerardo [Dipartimento di Fisica ' E R Caianiello' , Universita degli Studi di Salerno (Italy)
2007-07-13
We investigate the action of local unitary operations on multimode (pure or mixed) Gaussian states and single out the minimal number of locally invariant parameters which completely characterize the covariance matrix of such states. For pure Gaussian states, central resources for continuous-variable quantum information, we investigate separately the parameter reduction due to the additional constraint of global purity, and the one following by the local-unitary freedom. Counting arguments and insights from the phase-space Schmidt decomposition and in general from the framework of symplectic analysis, accompany our description of the standard form of pure n-mode Gaussian states. In particular, we clarify why only in pure states with n {<=} 3 modes all the direct correlations between position and momentum operators can be set to zero by local unitary operations. For any n, the emerging minimal set of parameters contains complete information about all forms of entanglement in the corresponding states. An efficient state engineering scheme (able to encode direct correlations between position and momentum operators as well) is proposed to produce entangled multimode Gaussian resources, its number of optical elements matching the minimal number of locally invariant degrees of freedom of general pure n-mode Gaussian states. Finally, we demonstrate that so-called 'block-diagonal' Gaussian states, without direct correlations between position and momentum, are systematically less entangled, on average, than arbitrary pure Gaussian states.
Continuous Variable Entanglement of Orbital Angular Momentum States
Lassen, Mikael Østergaard; Leuchs, G.; Andersen, Ulrik Lund
2009-01-01
We have generated a new quantum state of light composed of quadrature entangled Laguerre-Gaussian (LG) modes. For the generation we used an OPO operating in a new regime where all field parameters are degenerate except for its spatial degree of freedom for which it is two-fold degenerate. The ent...
Preparation of Two-Qutrit Entangled State in Cavity QED
LIN Xiu-Min; ZHOU Zheng-Wei; WU Yu-Chun; WANG Cheng-Zhi; GUO Guang-Can
2005-01-01
@@ We propose a scheme to generate a 3 × 3-dimensional maximally entangled state of two particles. Two three-level atoms interact with a strongly detuned cavity so that the cavity is only virtually excited and efficient decoherence time of the cavity is greatly prolonged. Compared to other protocols, this protocol is simpler and has a higher fidelity.
New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics
KUANG Mai-Hua; MA Shan-Jun; LIU Dong-Mei
2008-01-01
Based on the technique of integral within an ordered product of nonlinear bosonic operators, we construct a new kind of tripartite nonlinear entangled state |α,γ>λ in 3-mode Fock space, which can make up a complete set. We also simply discuss its properties and application.
Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States
Lassen, Mikael Østergaard; Leuchs, Gerd; Andersen, Ulrik Lund
2009-01-01
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital...
Transfers of entanglement qudit states in quantum networks
Sawerwain, Marek
2013-01-01
The issue of quantum states' transfer -- in particular, for so-called Perfect State Transfer (PST) -- in the networks represented by the spin chains seems to be one of the major concerns in quantum computing. Especially, in the context of future communication methods that can be used in broadly defined computer science. The chapter presents a definition of Hamiltonian describing the dynamics of quantum data transfer in one-dimensional spin chain, which is able to transfer the state of unknown qudits. The main part of the chapter is the discussion about possibility of entangled states' perfect transfer, in particular, for the generalized Bell states for qudits. One of the sections also contains the results of numerical experiments for the transmission of quantum entangled state in a noisy quantum channel.
Decoherence of Entangled States Calculated by a Systematic Approximate Method
LIU Tao; FAN Yun-Xia; HUANG Shu-Weng; WANG Ke-Lin; WANG Yi
2007-01-01
In this paper the coherent-state approximation (CA) method is used to deal with the problem of the decoherence of the entangled states of two two-state systems. As the base of the discussion, the dissipation of one two-state system has been investigated at first. The improved results calculated by CA are given in the paper. It is shown that the right approaching behavior and scaling law have been obtained when CA is applied to the problem of dissipation of two two-state systems coupled with environment. The whole evolution process and calculated results of the decoherence of the entangled states show also the scaling law, right approaching behavior, and rich phenomenon.
Ran, Du; Hu, Chang-Sheng; Yang, Zhen-Biao
2016-08-24
We study the entanglement transfer from a two-mode continuous variable system (initially in the two-mode SU(2) cat states) to a couple of discrete two-state systems (initially in an arbitrary mixed state), by use of the resonant Jaynes-Cummings (JC) interaction. We first quantitatively connect the entanglement transfer to non-Gaussianity of the two-mode SU(2) cat states and find a positive correlation between them. We then investigate the behaviors of the entanglement transfer and find that it is dependent on the initial state of the discrete systems. We also find that the largest possible value of the transferred entanglement exhibits a variety of behaviors for different photon number as well as for the phase angle of the two-mode SU(2) cat states. We finally consider the influences of the noise on the transferred entanglement.
Direct measurement of the Concurrence of spin-entangled states in a cavity–quantum dot system
Dong, Ping, E-mail: dongping9979@163.com [School of Electronic and Information Engineering, Hefei Normal University, Hefei 230061 (China); Liu, Jun, E-mail: junl@hftc.edu.cn [School of Electronic and Information Engineering, Hefei Normal University, Hefei 230061 (China); Zhang, Li-Hua [School of Physics and Electrical Engineering, Anqing Normal University, Anqing 246011 (China); Cao, Zhuo-Liang [School of Electronic and Information Engineering, Hefei Normal University, Hefei 230061 (China)
2016-08-15
A scheme for implementing the direct measurement of Concurrence is given in a cavity–quantum dot system. The scenario not only can directly measure the Concurrence of two-spin pure entangled state, but also suitable for the case of mixed state. More importantly, all of the operations are of geometric nature, which depend on the cavity-state-free evolution and can be robust against random operation errors. Our scheme provided an alternative method for directly measuring the degree of entanglement in solid-state system.
Tahira, Rabia; Ikram, Manzoor; Zubairy, M Suhail [Centre for Quantum Physics, COMSATS Institute of Information Technology, Islamabad (Pakistan); Bougouffa, Smail [Department of Physics, Faculty of Science, Taibah University, PO Box 30002, Madinah (Saudi Arabia)
2010-02-14
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
Controlled Probabilistic Teleportation of an Unknown Multi-Particle High-Dimensional Entangled State
SHI Jin; ZHAN You-Bang
2009-01-01
We propose a protocol for controlled probabilistic teleportation of an unknown tripartite qutrit entangled state with two partial tripartite qutrit entangled states as the quantum channel. It is found that teleportation associ-ated with the generalized qutrit Bell-basis measurement, the generalized qutrit π-state measurement and the generalized Hadamard operator in three-dimensional Hilbert space. We generalize the protocol for controlled probabilistic telepor-ration of an unknown k-particle qudit entangled state with a multi-particle qudit entangled state and a tripartite qudit entangled state as the quantum channel. We also calculate the classical communication cost required in both cases.
Description of rank four PPT entangled states of two qutrits
Chen, Lin
2011-01-01
It is known that some two qutrit entangled states of rank 4 with positive partial transpose [PPT] can be built from the unextendible product bases [UPB]. We show that this fact is indeed universal, namely all such states can be constructed from UPB. We also classify the 5-dimensional subspaces of two qutrits which contain only finitely many product states (up to scalar multiples), including those spanned by a UPB.
All pure bipartite entangled states can be self-tested
Coladangelo, Andrea; Goh, Koon Tong; Scarani, Valerio
2017-05-01
Quantum technologies promise advantages over their classical counterparts in the fields of computation, security and sensing. It is thus desirable that classical users are able to obtain guarantees on quantum devices, even without any knowledge of their inner workings. That such classical certification is possible at all is remarkable: it is a consequence of the violation of Bell inequalities by entangled quantum systems. Device-independent self-testing refers to the most complete such certification: it enables a classical user to uniquely identify the quantum state shared by uncharacterized devices by simply inspecting the correlations of measurement outcomes. Self-testing was first demonstrated for the singlet state and a few other examples of self-testable states were reported in recent years. Here, we address the long-standing open question of whether every pure bipartite entangled state is self-testable. We answer it affirmatively by providing explicit self-testing correlations for all such states.
Adesso, G; Serafini, A; Adesso, Gerardo; Illuminati, Fabrizio; Serafini, Alessio
2005-01-01
We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communication and defines a measure of genuine tripartite entanglement. We analytically determine the residual contangle for arbitrary pure three-mode Gaussian states and study the distribution of quantum correlations for such states. ...
Generalized two-mode coherent-entangled state with real parameters
无
2009-01-01
The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x; λ> is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operator is derived, with its own squeezing properties. Furthermore, generalized P-representation in the coherent-entangled state is constructed. Finally, it is revealed that superposition of the coherent-entangled states may produce the EPR entangled state.
Generation of various multiatom entangled graph states via resonant interactions
Dong Ping; Zhang Li-Hua; Cao Zhuo-Liang
2008-01-01
In this paper, a scheme for generating various multiatom entangled graph states via resonant interactions is proposed. We investigate the generation of various four-atom graph states first in the ideal case and then in the case in which the cavity decay and atomic spontaneous emission are taken into consideration in the process of interaction. More importantly, we improve the possible distortion of the graph states coming from cavity decay and atomic spontaneous emission by performing appropriate unitary transforms on atoms. The generation of multiatom entangled graph states is very important for constructing quantum one-way computer in a fault-tolerant manner. The resonant interaction time is very short, which is important in the sense of decoherence. Our scheme is easy and feasible within the reach of current experimental technology.
Holographic entanglement and causal information in coherent states
Gentle, Simon A. [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States); Rangamani, Mukund [Centre for Particle Theory & Department of Mathematical Sciences, Lower Mountjoy, South Road, Durham DH1 3LE (United Kingdom)
2014-01-22
Scalar solitons in global AdS{sub 4} are holographically dual to coherent states carrying a non-trivial condensate of a scalar operator. We study the holographic information content of these states, focusing on a particular spatial region, by examining the entanglement entropy and causal holographic information. We show generically that whenever the dimension of the condensed operator is sufficiently low (characterized by the double-trace operator becoming relevant), such coherent states have lower entanglement and causal holographic information than the vacuum state of the system, despite having greater energy. We also use these geometries to illustrate the fact that causal wedges associated with a simply-connected boundary region can have non-trivial topology even in causally trivial spacetimes.
The decoherence of quantum entanglement and teleportation in Bell-diagonal states
QIN Meng; LI Yan-Biao; WANG Xiao; BAI Zhong
2012-01-01
We study the dynamics of entanglement and teleportation in Bell-diagonal states. Using the concepts of concurrence and fidelity,the analytical expressions of the entanglement,the output entanglement and the average fidelity with decoherence are obtained for this model.We discover a class of initial states in which the output entanglement and the average fidelity are destroyed by decoherence. The quality of teleportation depends on the system parameters and time.
Remote preparation of a Greenberger-Home-Zeilinger state via a two-particle entangled state
Li Hong-Cai; Lin Xiu-Min; Li Xing-Min Hua; Yang Rang-Can
2007-01-01
We present two schemes for realizing the remote preparation of a Greenberger- Home- Zeilinger (GHZ) state. The first scheme is to remotely prepare a general N-particle GHZ state with two steps. One is to prepare a qubit state by using finite classical bits from sender to receiver via a two-particle entangled state, and the other is that the receiver introduces N - 1 additional particles and performs N - 1 controlled-not (C-Not) operations. The second scheme is to remotely prepare an JV-atom GHZ state via a two-atom entangled state in cavity quantum electrodynamics (QED). The two schemes require only a two-particle entangled state used as a quantum channel, so we reduce the requirement for entanglement.
Accessible quantification of multiparticle entanglement
Cianciaruso, Marco; Adesso, Gerardo
2015-01-01
Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology, and life sciences. For arbitrary multiparticle systems, the quantification of entanglement typically involves hard optimisation problems, and requires demanding tomographical techniques. In this paper we show that such difficulties can be overcome by developing an experimentally friendly method to evaluate measures of multiparticle entanglement via a geometric approach. The method provides exact analytical results for a relevant class of mixed states of $N$ qubits, and computable lower bounds to entanglement for any general state. For practical purposes, the entanglement determination requires local measurements in just three settings for any $N$. We demonstrate the power of our approach to quantify multiparticle entanglement in $N$-qubit bound entangled states and other states recently engineered in laboratory using quant...
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.
Separability of Pure and Mixed States of the Quantum Network of Four Nodes
QIANShang-Wu; GUZhi-Yu
2003-01-01
This article discusses the separability of the pure and mixed states of the quantum network of four nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.
Separability of Pure and Mixed States of the Quantum Network of Four Nodes
QIAN Shang-Wu; GU Zhi-Yu
2003-01-01
This article discusses the separability of the pure and mixed states of the quantum network of four nodesby means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.
Separability of Mixed States of the Quantum Network of Three Nodes
GU Zhi-Yu; QIAN Shang-Wu
2003-01-01
This article discusses the complete separability and partial separability of the mixed states of quantumnetwork of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantumnetwork theory.
Yu, Nengkun; Ying, Mingsheng
2011-01-01
In order to better understand the class of quantum operations that preserve the positivity of partial transpose (PPT operations) and its relation to the widely used class of local operations and classical communication (LOCC), we study the problem of distinguishing orthogonal maximally entangled states (MES) by PPT operations. Firstly, we outline a rather simple proof to show that the number of $d\\otimes d$ PPT distinguishable MES is at most $d$, which slightly generalizes existing results on this problem. Secondly, we construct 4 MES in $4\\otimes 4$ state space that cannot be distinguished by PPT operations. Before our work, it was unknown whether there exists $d$ MES in $d\\otimes d$ state space that are locally indistinguishable. This example leads us to a novel phenomenon of "Entanglement Catalysis Discrimination". Moreover, we find there exists a set of locally indistinguishable states $K$ such that $K^{\\otimes m}$ is locally distinguishable for some finite $m$. As an interesting application, we exhibit a...
Poddubny, Alexander N.; Sukhorukov, Andrey A.
2015-09-01
The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures. Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states. [1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014) [2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006). [3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014) [4] L.-G. Helt, J.E. Sipe and M.J. Steel, ar
Entanglement degradation in the solid state: Interplay of adiabatic and quantum noise
Bellomo, B.; Compagno, G.; D'Arrigo, A.; Falci, G.; Lo Franco, R.; Paladino, E.
2010-06-01
We study entanglement degradation of two noninteracting qubits subject to independent baths with broadband spectra typical of solid-state nanodevices. We obtain the analytic form of the concurrence in the presence of adiabatic noise for classes of entangled initial states presently achievable in experiments. We find that adiabatic (low-frequency) noise affects entanglement reduction analogously to pure dephasing noise. Due to quantum (high-frequency) noise, entanglement is totally lost in a state-dependent finite time. The possibility of implementing on-chip local and entangling operations is briefly discussed.
Entanglement degradation in the solid state: interplay of adiabatic and quantum noise
Bellomo, B; D'Arrigo, A; Falci, G; Franco, R Lo; Paladino, E
2010-01-01
We study entanglement degradation of two non-interacting qubits subject to independent baths with broadband spectra typical of solid state nanodevices. We obtain the analytic form of the concurrence in the presence of adiabatic noise for classes of entangled initial states presently achievable in experiments. We find that adiabatic (low frequency) noise affects entanglement reduction analogously to pure dephasing noise. Due to quantum (high frequency) noise, entanglement is totally lost in a state-dependent finite time. The possibility to implement on-chip both local and entangling operations is briefly discussed.
Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain
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.
Bartkiewicz, Karol; Lemr, Karel; Černoch, Antonín; Miranowicz, Adam
2017-03-01
We propose and experimentally implement an efficient procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995), 10.1016/0375-9601(95)00214-N] and the fully entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996), 10.1103/PhysRevA.54.3824] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. This is an experimental determination of these quantities without quantum state tomography or continuous monitoring of all measurement bases in the usual CHSH inequality tests. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measure these witnesses and estimate the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.
Werner State Structure and Entanglement Classification
David W. Lyons
2012-01-01
Full Text Available We present applications of the representation theory of Lie groups to the analysis of structure and local unitary classification of Werner states, sometimes called the decoherence-free states, which are states of n quantum bits left unchanged by local transformations that are the same on each particle. We introduce a multiqubit generalization of the singlet state and a construction that assembles these qubits into Werner states.
Cornering Gapless Quantum States via Their Torus Entanglement
Witczak-Krempa, William; Hayward Sierens, Lauren E.; Melko, Roger G.
2017-02-01
The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by χ . Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for χ in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansätze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansätze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model.
Tripartite entangled plaquette state in a cluster magnet
Carrasquilla, Juan; Chen, Gang; Melko, Roger G.
2017-08-01
Using large-scale quantum Monte Carlo simulations we show that a spin-1/2 X X Z model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break U (1 ) and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate LiZn2Mo3O8 , as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.
Spin Squeezing and Entanglement of Many-Particle Spin-Half States
YAN Dong; WANG Xiao-Guang; WU Ling-An
2005-01-01
@@ In many-particle spin-half systems with exchange symmetry, we find that the spin squeezing is related to two types of entanglement, the bipartite and the pairwise entanglement. A quantitative relationship is revealed for the spin squeezing parameter, the tangle, and the concurrence. We find that a class of states is spin squeezed if the pairwise entanglement is stronger than the bipartite entanglement.
Building projected entangled pair states with a local gauge symmetry
Zohar, Erez; Burrello, Michele
2016-04-01
Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.
Building Projected Entangled Pair States with a Local Gauge Symmetry
Zohar, Erez
2015-01-01
Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.
Quantum Private Comparison Protocol Based on Bell Entangled States
刘文; 王永滨; 崔巍
2012-01-01
In this paper,a quantum private comparison protocol is proposed based on bell entangled states.In our protocol,two parties can compare the equality of their information with the help of a semi-honest third party.The correctness and security of our protocol are discussed.One party cannot learn the other＇s private information and the third party also cannot learn any information about the private information.
Entanglement distillation for atomic states via cavity QED
Yang, Ming; Song, Wei; Cao, Zhuo-Liang
2004-10-01
Following a recent proposal (Phys. Rev. Lett. 85 (2000) 2392) about quantum information processing using dispersive atom-cavity interaction, in this paper, we proposed a physical scheme to concentrate the pure non-maximally entangled atomic states via cavity QED by using atomic collision in a far-off-resonant cavity. The most distinctive advantage of our scheme is that there is no excitation of cavity mode during the distillation procedure. Therefore the requirement on the quality of cavity is greatly loosened.
Is It Possible to Disentangle an Entangled Quantum State?
Chu, S Y
1998-01-01
Experimental tests of the suggestion that the generalization of Wheeler and Feynman's time symmetric system is the dynamical basis underlying quantum mechanics are considered. In a time-symmetric system, the instantaneous correlations exhibited by two spatially separated particles in an entangled state can be established through other particles, and can reveal advanced interaction effects. In particular, the existence of advanced gravity waves may be detectable through suitable arrangements at the Laser Interferometer Gravitation- Wave Observatory.
Properties and Application of Intermediate Entangled State Representation
PANG Qian-Jun
2005-01-01
@@ We introduce the intermediate entangled state |α> and discuss its properties of|α>λ,ν. We obtain the expression of the two-mode Wigner operator in the |α>λ,ν representation. We find that the projection operator |α>λ,νλ,ν λ,ν representation, we successfully obtain the eigenvalues and eigenvectors of a bipartite system coupled in a quite complicated way.
Multipartite Continuous-Variable Entanglement Distribution with Separable Gaussian States
Zeng, Chuan; Zhang, Jian-Zhong; Xie, Shu-Cui
2017-03-01
In this paper, a quantum proxy blind signature scheme based on controlled quantum teleportation is proposed. This scheme uses a genuine five-qubit entangled state as quantum channel and adopts the classical Vernam algorithm to blind message. We use the physical characteristics of quantum mechanics to implement delegation, signature and verification. Security analysis shows that our scheme is valid and satisfy the properties of a proxy blind signature, such as blindness, verifiability, unforgeability, undeniability.
YUAN Hong-Chun; QI Kai-Guo
2005-01-01
We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.
Induced Quantum Entanglement of Nuclear Metastable States of 115In
Van Gent, D L
2004-01-01
Experiments conducted in our laboratory conclusively demonstrated that at least 20% of 115In metastable states become quantum entangled (QE) during gamma photo-excitation processes where a significant fraction of the photo-excitation gamma (E > 1.02 MeV) are QE. In addition, it was found that the half-life of 115mIn populations in identical photo-excited indium foils varied as much as 70% depending on whether the 99.999% purity indium foils were photo-excited with a High Intensity 60Co Source (HICS) or a Varian CLINAC (Compact Linear Accelerator) with average energy 2 MeV and maximum energy 6 MeV Bremsstrahlung photo-excitation quanta. Decay kinetics of 115mIn populations in indium foils demonstrate that these metastable states are primarily QE in pairs when photo-excited in the HICS apparatus and at higher orders of entanglement of triplets and possibly quadruplets when photo-excited with the CLINAC. It appears that QE gamma photons can transfer quantum entangled properties to radioactive metastable states.
Entanglement Transfer via Heisenberg Interaction in a Four-Qubit System
REN Feng-Hua; WANG Zhao-Ming
2007-01-01
We investigate the entanglement transfer in a four-qubit system and calculate the concurrence between any two qubits in different initial states.We show that both the pure entangled state and mixed entangled state can be transferred.For some special coupling constants and some evolution time,entanglement can be completely transferred from one pair particles to another.
Dynamics of quantum entanglement
Zyczkowski, K; Horodecki, M; Horodecki, R; Zyczkowski, Karol; Horodecki, Pawel; Horodecki, Michal; Horodecki, Ryszard
2002-01-01
A model of discrete dynamics of entanglement of bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied with an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of both subsystems. For some mixed states having different marginal entropies of both subsystems (one larger than the global entropy and one smaller) we find an asymmetry in speed of entanglement decay. The entanglement of these states decreases faster, if the depolarizing channel acts on the "classical" subsystem, characterized by smaller marginal entropy.
[Mixed states and neuroimaging].
Kaladjian, A; Belzeaux, R; Micoulaud-Franchi, J A; Cermolacce, M; Fakra, E; Azorin, J-M
2013-12-01
Despite the growing number of neuroimaging studies in bipolar disorder over the past years, the brain regions involved in mood dysregulation in this disease are still poorly understood. If some neurofunctional abnormalities seem to be independent of mood state, others were preferentially associated with mania or depression, involving the amygdala and other limbic regions as well as ventral frontal regions, with a likely hemispheric lateralization of these abnormalities according to the thymic state that was examined. Very few imaging studies became interested in bipolar patients in a mixed state, making it harder to connect brain malfunction to a given mood state. However, data obtained so far support the hypothesis of a lateralization of brain abnormalities in relation to bipolar symptomatology, suggesting that neurofonctional abnormalities preferentially located in the right ventral frontal and limbic areas may underlie the depressive component, associated with abnormalities of the left similar regions for the manic component. Identification of brain dysfunctions that may explain the emergence of mixed symptoms will likely provide useful information to better understand the respective roles of each hemisphere in the pathophysiology of bipolar disorder. Copyright © 2013 Sociedade Brasileira de Farmacognosia. Published by Elsevier Masson SAS.. All rights reserved.
Adesso, Gerardo; Serafini, Alessio; Illuminati, Fabrizio
2006-03-01
We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequality constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.
Separability of Pure States and Mixed States of the Quantum Network of Two Nodes
GU Zhi-Yu; QIAN Shang-Wu
2003-01-01
This article discusses the separability of the pure states and mixed states of the quantum network of twonodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum networktheory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor Mjk(1, 2) is equal to zerofor all possible j and k.
Semiclassical Wigner distribution for two-mode entangled state
Dechoum, K; Vallejos, R O; Khoury, A Z; 10.1103/PhysRevA.81.043834
2011-01-01
We derive the steady state solution of the Fokker-Planck equation that describes the dynamics of the nondegenerate optical parametric oscillator in the truncated Wigner representation of the density operator. We assume that the pump mode is strongly damped, which permits its adiabatic elimination. When the elimination is correctly executed, the resulting stochastic equations contain multiplicative noise terms, and do not admit a potential solution. However, we develop an heuristic scheme leading to a satisfactory steady-state solution. This provides a clear view of the intracavity two-mode entangled state valid in all operating regimes of the OPO. A nongaussian distribution is obtained for the above threshold solution.
Remote State Preparation via a Non-Maximally Entangled Channel
郑亦庄; 顾永建; 郭光灿
2002-01-01
We investigate remote state preparation (RSP) via a non-maximally entangled channel for three cases: a general qubit; a special ensemble of qubits (qubit states on the equator of the Bloch sphere); and an asymptotic limit of N copies ofa general state. The results show that the classical communication cost of RSP for the two latter cases can be less than that of teleportation, but for the first case, in a restricted setting, the classical communication cost is equal to that of teleportation. Whether or not this is the case for a more general setting is still an open question.
Entanglement in neutrino oscillations
Blasone, M.; Dell' Anno, F.; De Siena, S.; Illuminati, F. [Universita degli Studi di Salerno Via Ponte don Melillon, Dipt. di Matematica e Informatica, Fisciano SA (Italy); INFN Sezione di Napoli, Gruppo collegato di Salerno - Baronissi SA (Italy); Dell' Anno, F.; De Siena, S.; Illuminati, F. [CNR-INFM Coherentia - Napoli (Italy); Blasone, M. [ISI Foundation for Scientific Interchange, Torino (Italy)
2009-03-15
Flavor oscillations in elementary particle physics are related to multimode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks. (authors)
Conservation relation of nonclassicality and entanglement for Gaussian states in a beam splitter
Ge, Wenchao; Tasgin, Mehmet Emre; Zubairy, M. Suhail
2015-11-01
We study the relation between single-mode nonclassicality and two-mode entanglement in a beam splitter. We show that single-mode nonclassicality (the entanglement potential) of incident light cannot be transformed into two-mode entanglement completely after a single beam splitter. Some of the entanglement potential remains as single-mode nonclassicality in the two entangled output modes. Two-mode entanglement generated in the process can be equivalently quantified as an increase in the minimum uncertainty widths (or decrease in the squeezing) of the output states compared to the input states. We use the nonclassical depth and logarithmic negativity as single-mode nonclassicality and entanglement measures, respectively. We realize that a conservation relation between the two quantities can be adopted for Gaussian states, if one works in terms of uncertainty width. This conservation relation is extended to many sets of beam splitters.
Entangled photon generation using four-wave mixing in azimuthally symmetric microresonators.
Camacho, Ryan M
2012-09-24
A novel quantum mechanical formulation of the bi-photon wavefunction and spectra resulting from four-wave mixing is developed for azimuthally symmetric systems. Numerical calculations are performed verifying the use of the angular group velocity and angular group velocity dispersion in such systems, as opposed their commonly used linear counterparts. The dispersion profile and bi-photon spectra of two illustrative examples are given, emphasizing the physical origin of the effects leading to the conditions for angular momentum and energy conservation. A scheme is proposed in which widely spaced narrowband entangled photons may be produced through a four-wave mixing process in a chip-scale ring resonator. The entangled photon pairs are found to conserve energy and momentum in the four-wave mixing interaction, even though both photon modes lie in spectral regions of steep angular group velocity dispersion.
Gaussian measures of entanglement versus negativities and the ordering of two-mode Gaussian states
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
In this work we focus on entanglement of two--mode Gaussian states of continuous variable systems. We introduce the formalism of Gaussian entanglement measures, adopting the framework developed in [M. M. Wolf {\\em et al.}, Phys. Rev. A {\\bf 69}, 052320 (2004)], where the Gaussian entanglement of formation was defined. We compute Gaussian measures explicitely for two important families of nonsymmetric two--mode Gaussian states, namely the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in [G. Adesso {\\em et al.}, Phys. Rev. Lett. {\\bf 92}, 087901 (2004)]. This allows us to compare the {\\em orderings} induced on the set of entangled two--mode Gaussian states by the negativities and by the Gaussian entanglement measures. We find that in a certain range of global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement than states of maximum negativity. Thus ...
Rotationally invariant bipartite states and bound entanglement
Augusiak, R; Augusiak, Remigiusz; Stasi\\'{n}ska, Julia
2007-01-01
We consider rotationally invariant states in $\\mathbb{C}^{N_{1}}\\ot \\mathbb{C}^{N_{2}}$ Hilbert space with even $N_{1}\\geq 4$ and arbitrary $N_{2}\\geq N_{1}$, and show that in such case there always exist states which are inseparable and remain positive after partial transposition, and thus the PPT criterion does not suffice to prove separability of such systems. We demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys. Rev. Lett {\\bf 97}, 080501 (2006)] to states that remain invariant after partial time reversal.
Exact and Asymptotic Measures of Multipartite Pure State Entanglement
Bennett, C H; Rohrlich, D E; Smolin, J A; Thapliyal, A V; Bennett, Charles H.; Popescu, Sandu; Rohrlich, Daniel; Smolin, John A.; Thapliyal, Ashish V.
1999-01-01
In an effort to simplify the classification of pure entangled states of multi (m) -partite quantum systems, we study exactly and asymptotically (in n) reversible transformations among n'th tensor powers of such states (ie n copies of the state shared among the same m parties) under local quantum operations and classical communication (LOCC). With regard to exact transformations, we show that two states whose 1-party entropies agree are either locally-unitarily (LU) equivalent or else LOCC-incomparable. Asymptotic transformations result in a simpler classification than exact transformations. We show that m-partite pure states having an m-way Schmidt decomposition are simply parameterizable, with the partial entropy across any nontrivial partition representing the number of standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the state in question. For general m-partite states, partial entropies across different partitions need not be equal, and since partial entropies are conserved by asymp...
Bounds on entanglement in qudit subsystems
Kendon, V M; Munro, W J; Kendon, Vivien M; Zyczkowski, Karol; Munro, William J
2002-01-01
The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other N-m qudits. We examine the entanglement in this mixed space of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than N/3 qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than N/3 falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.
Distillability and PPT entanglement of low-rank quantum states
Chen, Lin
2011-01-01
It is well-known that bipartite quantum states, whose rank is strictly smaller than the maximum of the ranks of the reduced states, is 1-distillable by local operations and classical communication. Our first main result is that this is also true for states with rank equal to this maximum. This was conjectured in 1999 in the special case when the two local ranks are equal. From our main result we obtain a new constraint on the monogamy of entanglement: a tripartite pure state cannot have two entangled undistillable reduced bipartite density operators. We also prove that the so called checkerboard states are 1-distillable if and only if they are NPT, i.e., the partial transpose of the density matrix is not positive semidefinite. On the basis of this proof, we derive our second main result. Namely, bipartite states of rank 4 which are also PPT, i.e., have positive semidefinite partial transpose, are separable if and only their range contains a product state. This provides a complete solution of the separability ...
Entanglement in eight-qubit graph states
Cabello, Adan [Departamento de Fisica Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain)], E-mail: adan@us.es; Lopez-Tarrida, Antonio J.; Moreno, Pilar [Departamento de Fisica Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain); Portillo, Jose R. [Departamento de Matematica Aplicada I, Universidad de Sevilla, E-41012 Sevilla (Spain)
2009-06-15
Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for its preparation, and calculate the Schmidt measure for the 8-partite split, and the Schmidt ranks for all bipartite splits. This results into an extension to 8 qubits of the classification of graph states proposed by Hein, Eisert, and Briegel [M. Hein, J. Eisert, H.J. Briegel, Phys. Rev. A 69 (2004) 062311].
Transformation of bipartite non-maximally entangled states into a tripartiteWstate in cavity QED
ZANG XUE-PING; YANG MING; DU CHAO-QUN; WANG MIN; FANG SHU-DONG; CAO ZHUO-LIANG
2016-05-01
We present two schemes for transforming bipartite non-maximally entangled states into a W state in cavity QED system, by using highly detuned interactions and the resonant interactions between two-level atoms and a single-mode cavity field. A tri-atom W state can be generated by adjusting the interaction times between atoms and the cavity mode. These schemes demonstrate that two bipartite non-maximally entangled states can be merged into a maximally entangled W state. So the scheme can, in some sense, be regarded as an entanglement concentration process. The experimental feasibility of the schemes is also discussed.
Characterizing symmetries in a projected entangled pair state
Perez-Garcia, D; Gonzalez-Guillen, C E [Departamento Analisis Matematico and IMI, Universidad Complutense de Madrid, 28040 Madrid (Spain); Sanz, M; Cirac, J I [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching (Germany); Wolf, M M [Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen (Denmark)], E-mail: dperez@mat.ucm.es
2010-02-15
We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective.
Information, Relative Entropy of Entanglement and Irreversibility
Henderson, L
2000-01-01
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this, relations between relative entropy of entanglement and mutual information are derived.
CHEN Chang-Yong; LI Shao-Hua
2007-01-01
A scheme for approximately and conditionally teleporting an unknown atomic-entangled state in cavity QED is proposed.It is the novel extension of the scheme of [Phys.Rev.A 69 (2004) 064302],where the state to be teleported is an unknown atomic state and where only a time point of system evolution and the corresponding fidelity implementing the teleportation are given.In fact,there exists multi-time points and the corresponding fidclities,which are shown in this paper and then are used to realize the approximate and conditional teleportation of the unknown atomic-entangled state.Naturally,our scheme does not involve the Bell-state measurement or an additional atom,which is required in the Bell-state measurement,only requiring one single-mode cavity.The scheme may be generalized to not only the teleportation of the cavity-mode-entangled-state by means of a single atom but also the teleportation of the unknown trapped-ion-entangled-state in a linear ion trap and the teleportation of the multi-atomic entangled states included in generalized GHZ states.
Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
Orus, Roman
2011-01-01
Here we evaluate the many-body entanglement properties of a generalized SU(n) valence bond solid state on a chain. Our results follow from a derivation of the transfer matrix of the system which, in combination with symmetry properties, allows for a new, elegant and straightforward evaluation of different entanglement measures. In particular, the geometric entanglement per block, correlation length, von Neumann and R\\'enyi entropies of a block, localizable entanglement and entanglement length are obtained in a very simple way. All our results are in agreement with previous derivations for the SU(2) case.
Stability of Flip and Exchange Symmetric Entangled State Classes
Zafer Gedik, Mehmet
2010-03-01
Flip and exchange symmetric (FES) many-qubit states, which can be obtained from a state with the same symmetries by means of invertible local operations (ILO), constitute a one-parameter family of curves in the Hilbert space. Eigenstates of FES ILOs correspond to vectors that cannot be transformed to other FES states. Therefore, equivalence classes of states under ILO can be determined in a systematic way for an arbitrary number of qubits. More important, for entangled states, at the boundaries of neighboring equivalence classes, one can show that when the fidelity between the final state after an ILO and a state of the neighboring class approaches unity, probability of success decreases to zero. In other words, the classes are stable under ILOs.
A generic source for multiphoton path entangled states
Afek, Itai; Silberberg, Yaron
2009-01-01
"Schrodinger's cat" is a gedankenexperiment intended to highlight conceptual difficulties in the interpretation of quantum mechanics. The generation of 'cat-like' states is central to numerous quantum information protocols. In particular, much attention has been drawn by states containing N photons in a superposition of all being in one of two designated modes. These maximally path entangled states, known as 'NOON' states, exhibit enhanced phase sensitivity and allow reaching the fundamental quantum limit of precision measurement. Such states could also be used for obtaining 'super-resolution' in quantum lithography. Creation of NOON states in the lab, has been limited to N=3. Surpassing this has proven a formidable experimental challenge. Here, we realize a scheme for generation of high fidelity NOON states with arbitrarily large N. We demonstrate the versatility of the scheme by measuring up to N=5 in a single setup, this is in contrast to previous experiments which were custom-designed for a specific N. Th...
Robustness in projected entangled pair states
Cirac, J. Ignacio; Michalakis, Spyridon; Pérez-García, David; Schuch, Norbert
2013-09-01
We analyze a criterion which guarantees that the ground states of certain many-body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restricted version of the local topological quantum order (LTQO) condition [Michalakis and Pytel, Commun. Math. Phys.10.1007/s00220-013-1762-6 322, 277 (2013)] provides a checkable criterion which allows us to assess the stability of local properties of PEPS under physical perturbations. We moreover show that LTQO itself is stable under perturbations which preserve the spectral gap, leading to nontrivial examples of PEPS which possess LTQO and are thus stable under arbitrary perturbations.
Experimental Entanglement and Nonlocality of a Two-Photon Six-Qubit Cluster State
Ceccarelli, Raino; De Martini, Francesco; Mataloni, Paolo; Cabello, Adan
2009-01-01
We create a six-qubit linear cluster state by transforming a two-photon hyper-entangled state in which three qubits are encoded in each particle, one in the polarization and two in linear momentum degrees of freedom. For this state, we demonstrate genuine six-qubit entanglement, robustness of entanglement against the loss of qubits, and higher violation of Bell inequalities than in previous experiments.
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
Entanglement Dynamics of Two Qubits Coupled to a Noise Environmen
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.
Remote Preparation of Multipartite Equatorial Entangled States in High Dimensions with Three Parties
HOU Kui; WANG Jing; SHI Shou-Hua
2009-01-01
A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N - 1 pairs of bipartite d-dimensional non-maximally entangled states and a tripartite d-dimension non-maximally entangled state. It is shown that the sender can help either of the two receivers to remotely prepare the original state, and the N-particle projective measurement and the genera//zed Hadamard transformation are needed in this scheme. The total success probability and classical communication cost are calculated.
Double-lambda microscopic model for entangled light generation by four-wave-mixing
Glorieux, Q; Guibal, S; Guidoni, L; Likforman, J -P; Coudreau, T; Arimondo, E
2010-01-01
Motivated by recent experiments, we study four-wave-mixing in an atomic double-{\\Lambda} system driven by a far-detuned pump. Using the Heisenberg-Langevin formalism, and based on the microscopic properties of the medium, we calculate the classical and quantum properties of seed and conju- gate beams beyond the linear amplifier approximation. A continuous variable approach gives us access to relative-intensity noise spectra that can be directly compared to experiments. Restricting ourselves to the cold-atom regime, we predict the generation of quantum-correlated beams with a relative-intensity noise spectrum well below the standard quantum limit (down to -6 dB). Moreover entanglement between seed and conjugate beams measured by an inseparability down to 0.25 is expected. This work opens the way to the generation of entangled beams by four-wave mixing in a cold atomic sample.
Experimental generation of tripartite polarization entangled states of bright optical beams
Wu, Liang; Yan, Zhihui; Liu, Yanhong; Deng, Ruijie; Jia, Xiaojun; Xie, Changde; Peng, Kunchi
2016-04-01
The multipartite polarization entangled states of bright optical beams directly associating with the spin states of atomic ensembles are one of the essential resources in the future quantum information networks, which can be conveniently utilized to transfer and convert quantum states across a network composed of many atomic nodes. In this letter, we present the experimental demonstration of tripartite polarization entanglement described by Stokes operators of optical field. The tripartite entangled states of light at the frequency resonant with D1 line of Rubidium atoms are transformed into the continuous variable polarization entanglement among three bright optical beams via an optical beam splitter network. The obtained entanglement is confirmed by the extended criterion for polarization entanglement of multipartite quantized optical modes.
Note on Entanglement of an Arbitrary State of Two Qubits
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.
Quantum memory for entangled continuous-variable states
Jensen, K.; Wasilewski, W.; Krauter, H.; Fernholz, T.; Nielsen, B. M.; Owari, M.; Plenio, M. B.; Serafini, A.; Wolf, M. M.; Polzik, E. S.
2011-01-01
A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are versatility (allowing a wide range of inputs) and preservation of quantum information in a way unattainable with any classical memory device. Here we demonstrate such a quantum memory for continuous-variable entangled states, which play a fundamental role in quantum information processing. We store an extensive alphabet of two-mode 6.0dB squeezed states obtained by varying the orientation of squeezing and the displacement of the states. The two components of the entangled state are stored in two room-temperature cells separated by 0.5m, one for each mode, with a memory time of 1ms. The true quantum character of the memory is rigorously proved by showing that the experimental memory fidelity 0.52+/-0.02 significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements.
Entanglement and extreme spin squeezing of unpolarized states
Vitagliano, Giuseppe; Apellaniz, Iagoba; Kleinmann, Matthias; Lücke, Bernd; Klempt, Carsten; Tóth, Géza
2017-01-01
We present criteria to detect the depth of entanglement in macroscopic ensembles of spin-j particles using the variance and second moments of the collective spin components. The class of states detected goes beyond traditional spin-squeezed states by including Dicke states and other unpolarized states. The criteria derived are easy to evaluate numerically even for systems of very many particles and outperform past approaches, especially in practical situations where noise is present. We also derive analytic lower bounds based on the linearization of our criteria, which make it possible to define spin-squeezing parameters for Dicke states. In addition, we obtain spin squeezing parameters also from the condition derived in (Sørensen and Mølmer 2001 Phys. Rev. Lett. 86 4431). We also extend our results to systems with fluctuating number of particles.
Tensor Rank and Stochastic Entanglement Catalysis for Multipartite Pure States
Chen, Lin; Duan, Runyao; Ji, Zhengfeng; Winter, Andreas
2010-01-01
The tensor rank (aka generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state $\\ket{W_3}=\\tfrac{1}{\\sqrt{3}}(\\ket{100}+\\ket{010}+\\ket{001})$ and its $N$-partite generalization $\\ket{W_N}$. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of $\\ket{W_3}$ has rank either 15 or 16, (ii) two copies of $\\ket{W_N}$ has rank $3N-2$, and (iii) $n$ copies of $\\ket{W_N}$ has rank O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple copy bunches or when assisted by some catalyzing state. This novel effect is impossible for bipartite pure states.
Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Yang, Hyeon; Choi, Seong-Gon
2017-01-01
We propose quantum information processing schemes based on cavity quantum electrodynamics (QED) for quantum communication. First, to generate entangled states (Bell and Greenberger-Horne-Zeilinger [GHZ] states) between flying photons and three-level atoms inside optical cavities, we utilize a controlled phase flip (CPF) gate that can be implemented via cavity QED). Subsequently, we present an entanglement swapping scheme that can be realized using single-qubit measurements and CPF gates via optical cavities. These schemes can be directly applied to construct an entanglement channel for a communication system between two users. Consequently, it is possible for the trust center, having quantum nodes, to accomplish the linked channel (entanglement channel) between the two separate long-distance users via the distribution of Bell states and entanglement swapping. Furthermore, in our schemes, the main physical component is the CPF gate between the photons and the three-level atoms in cavity QED, which is feasible in practice. Thus, our schemes can be experimentally realized with current technology.
Probabilistic teleportation of multi-particle partially entangled state
Chen Xiu-Bo; Du Jian-Zhong; Wen Qiao-Yan; Zhu Fu-Chen
2008-01-01
Utilizing the generalized measurement described by positive operator-valued measure, this paper comes up with a protocol for teleportation of an unknown multi-particle entangled (GHZ) state with a certain probability. The feature of the present protocol is to weaken requirement for the quantum channel initially shared by sender and receiver. All unitary transformations performed by receiver are summarized into a formula. On the other hand, this paper explicitlyconstructs the efficient quantum circuits for implementing the proposed teleportation by means of universal quantum logic operations in quantum computation.
How often is a random quantum state k-entangled?
Szarek, Stanislaw J; Zyczkowski, Karol
2010-01-01
The set of trace preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k=2,...,d. Working with the measure induced by the Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes of these sets. Our results strongly suggest that the inner set of (k+1)-positive maps forms a small fraction of the outer set of k-positive maps. These results are related to analogous bounds for the relative volume of the sets of k-entangled states describing a bipartite d X d system.
How often is a random quantum state k-entangled?
Szarek, Stanislaw J [Universite Pierre et Marie Curie, Paris (France); Werner, Elisabeth [Case Western Reserve University, Cleveland, OH 44106-7058 (United States); Zyczkowski, Karol, E-mail: szarek@cwru.edu [Institute of Physics, Jagiellonian University, ul Reymonta 4, 30-059 Krakow (Poland)
2011-01-28
The set of trace-preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k = 2, ..., d. Working with the measure induced by the Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes of these sets. Our results strongly suggest that the inner set of (k + 1) -positive maps forms a small fraction of the outer set of k-positive maps. These results are related to analogous bounds for the relative volume of the sets of k-entangled states describing a bipartite d x d system.
Ground-state entanglement in a three-spin transverse Ising model with energy current
Zhang Yong; Liu Dan; Long Gui-Lu
2007-01-01
The ground-state entanglement associated with a three-spin transverse Ising model is studied. By introducing an energy current into the system, a quantum phase transition to energy-current phase may be presented with the variation of external magnetic field; and the ground-state entanglement varies suddenly at the critical point of quantum phase transition. In our model, the introduction of energy current makes the entanglement between any two qubits become maximally robust.
Steady-state entanglement of a Bose-Einstein condensate and a nanomechanical resonator
Asjad, Muhammad; 10.1103/PhysRevA.84.033606
2011-01-01
We analyze the steady-state entanglement between Bose-Einstein condensate trapped inside an optical cavity with a moving end mirror (nanomechanical resonator) driven by a single mode laser. The quantized laser field mediates the interaction between the Bose-Einstein condensate and nanomechanical resonator. In particular, we study the influence of temperature on the entanglement of the coupled system, and note that the steady-state entanglement is fragile with respect to temperature.
Classification of bi-qutrit PPT entangled edge states by their ranks
Kte, Seung-Hyeok
2012-01-01
We construct $3\\otimes 3$ PPT entangled edge states with maximal ranks, to complete the classification of $3\\otimes 3$ PPT entangled edge states by their types. The ranks of the states and their partial transposes are 8 and 6, respectively. These examples also disprove claims in the literature.
Comparison of qubit and qutrit like entangled squeezed and coherent states of light
Najarbashi, G.; Mirzaei, S.
2016-10-01
Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trends are compared with those obtained for qubit and qutrit like entangled coherent states (ECS).
Teleportation of a Coherent Superposition State Via a nonmaximally Entangled Coherent Xhannel
无
2002-01-01
@@ We investigate the problemm of teleportation of a superposition coherent state with nonmaximally entangled coherent channel. Two strategies are considered to complete the task. The first one uses entanglement concentration to purify the channel to a maximally entangled one. The second one teleports the state through the nonmaximally entangled coherent channel directly. We find that the probabilities of successful teleportations for the two strategies are depend on the amplitudes of the coherent states and the mean fidelity of teleportation using the first strategy is always less than that of the second strategy.
Heralded entanglement between solid-state qubits separated by three metres.
Bernien, H; Hensen, B; Pfaff, W; Koolstra, G; Blok, M S; Robledo, L; Taminiau, T H; Markham, M; Twitchen, D J; Childress, L; Hanson, R
2013-05-01
Quantum entanglement between spatially separated objects is one of the most intriguing phenomena in physics. The outcomes of independent measurements on entangled objects show correlations that cannot be explained by classical physics. As well as being of fundamental interest, entanglement is a unique resource for quantum information processing and communication. Entangled quantum bits (qubits) can be used to share private information or implement quantum logical gates. Such capabilities are particularly useful when the entangled qubits are spatially separated, providing the opportunity to create highly connected quantum networks or extend quantum cryptography to long distances. Here we report entanglement of two electron spin qubits in diamond with a spatial separation of three metres. We establish this entanglement using a robust protocol based on creation of spin-photon entanglement at each location and a subsequent joint measurement of the photons. Detection of the photons heralds the projection of the spin qubits onto an entangled state. We verify the resulting non-local quantum correlations by performing single-shot readout on the qubits in different bases. The long-distance entanglement reported here can be combined with recently achieved initialization, readout and entanglement operations on local long-lived nuclear spin registers, paving the way for deterministic long-distance teleportation, quantum repeaters and extended quantum networks.
Preparation of Multi—Atom Entangled States with a Single Cavity in a Thermal State
ZHENGShi－Biao
2002-01-01
A scheme is suggested for the generation of multi-atom maximally entangled states with a cavity in a thermal state,In this scheme several appropriately prepared two-level atoms are simultaneously sent through the nonresonant cavity.We divide the whole atom-cavity interaction time into two equal parts.At the end of the first part a π pulse is applied to the atome using a classical field.Then the photon-number-dependent shifts on the atomic states are cancelled and the atomic system finally evoloves to a maximally entangled state.
Quantum entanglement between an optical photon and a solid-state spin qubit.
Togan, E; Chu, Y; Trifonov, A S; Jiang, L; Maze, J; Childress, L; Dutt, M V G; Sørensen, A S; Hemmer, P R; Zibrov, A S; Lukin, M D
2010-08-01
Quantum entanglement is among the most fascinating aspects of quantum theory. Entangled optical photons are now widely used for fundamental tests of quantum mechanics and applications such as quantum cryptography. Several recent experiments demonstrated entanglement of optical photons with trapped ions, atoms and atomic ensembles, which are then used to connect remote long-term memory nodes in distributed quantum networks. Here we realize quantum entanglement between the polarization of a single optical photon and a solid-state qubit associated with the single electronic spin of a nitrogen vacancy centre in diamond. Our experimental entanglement verification uses the quantum eraser technique, and demonstrates that a high degree of control over interactions between a solid-state qubit and the quantum light field can be achieved. The reported entanglement source can be used in studies of fundamental quantum phenomena and provides a key building block for the solid-state realization of quantum optical networks.
Quantum Secure Direct Communication with Five-Qubit Entangled State
LIN Song; GAO Fei; LIU Xiao-Fen
2011-01-01
Recently, a genuine five-qubit entangled state has been achieved by Brown et al.[J. Phys. A 38(2005)1119]. Later it was indicated that this state can be used for quantum teleportation and quantum state sharing. Here we build a quantum secure direct communication protocol with this state, and prove that it is secure in ideal conditions.In the protocol, the sender performs unitary transformations to encode a secret message on his/her particles and sends them to the receiver. The receiver then performs projective determinate measurement to decode the secret message directly.Fhrthermore, this protocol utilizes superdense coding to achieve a high intrinsic efficiency and source capacity.
Characterizing entanglement with global and marginal entropic measures
Adesso, G; De Siena, S; Adesso, Gerardo; Illuminati, Fabrizio; Siena, Silvio De
2003-01-01
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entaglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such states cannot be discriminated by the majorization criterion.
Distillable entanglement in d circle times d dimensions
Hamieh, S; Zaraket, H
2003-01-01
Distillable entanglement (E-d) is one of the acceptable measures of entanglement of mixed states. On the basis of discrimination through local operation and classical communication, this letter gives E-d for two classes of orthogonal multipartite maximally entangled states.
Bound entanglement and entanglement bounds
Sauer, Simeon [Physikalisch-Astronomische Fakultaet, Friedrich-Schiller-Univesitaet Jena (Germany)]|[Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg (Germany); Melo, Fernando de; Mintert, Florian; Buchleitner, Andreas [Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg (Germany)]|[Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Str.38, D-01187 Dresden (Germany); Bae, Joonwoo [School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-012 (Korea); Hiesmayr, Beatrix [Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)
2008-07-01
We investigate the separability of Bell-diagonal states of two qutrits. By using lower bounds to algebraically estimate concurrence, we find convex regions of bound entangled states. Some of these regions exactly coincide with the obtained results when employing optimal entanglement witnesses, what shows that the lower bound can serve as a precise detector of entanglement. Some hitherto unknown regions of bound entangled states were discovered with this approach, and delimited efficiently.
Explicit Analysis of Creating Maximally Entangled State in the Mott Insulator State
LI Min-Si; TIAN Li-Jun; ZHANG Hong-Biao
2004-01-01
@@ We clarify the essence of the method proposed by You (Phys. Rev. Lett. 90 (2004) 030402) to create the maximally entangled atomic N-GHZ state in the Mott insulator state. Based on the time-independent perturbation theory,we find that the validity of the method can be summarized as that the Hamiltonian governing the evolution is approximately equivalent to the type aJ2x + bJx, which is the well known form used to create the maximally entangled state.
Preparation of Multi-Atom Entangled States with a Single Cavity in a Thermal State
ZHENG Shi-Biao
2002-01-01
A scheme is suggested for the generation of multi-atom maximally entangled states with a cavity in a thermalstate. In this scheme several appropriately prepared two-level atoms are simultaneously sent through the nonresonantcavity. We divide the whole atom-cavity interaction time into two equal parts. At the end of the first part a π pulse isapplied to the atoms using a classical field. Then the photon-number-dependent shifts on the atomic states are cancelledand the atomic system finally evolves to a maximally entangled state.
Teleportation of an unknown bipartite state via non-maximally entangled two-particle state
Cao Hai-Jing; Guo Yan-Qing; Song He-Shan
2006-01-01
In this paper a new scheme for teleporting an unknown entangled state of two particles is proposed. To weaken the requirement for the quantum channel, without loss of generality, two communicators only share a non-maximally entangled two-particle state. Teleportation can be probabilistically realized if sender performs Bell-state measurements and Hadamard transformation and receiver introduces two auxiliary particles, operates G-not operation, single-qubit measurements and appropriate unitary transformations. The probability of successful teleportation is determined by the smaller one among the coefficients' absolute values of the quantum channel.
Continuous variable quantum key distribution with modulated entangled states
Madsen, Lars S; Usenko, Vladyslav C.; Lassen, Mikael
2012-01-01
Quantum key distribution enables two remote parties to grow a shared key, which they can use for unconditionally secure communication over a certain distance. The maximal distance depends on the loss and the excess noise of the connecting quantum channel. Several quantum key distribution schemes...... based on coherent states and continuous variable measurements are resilient to high loss in the channel, but are strongly affected by small amounts of channel excess noise. Here we propose and experimentally address a continuous variable quantum key distribution protocol that uses modulated fragile...... entangled states of light to greatly enhance the robustness to channel noise. We experimentally demonstrate that the resulting quantum key distribution protocol can tolerate more noise than the benchmark set by the ideal continuous variable coherent state protocol. Our scheme represents a very promising...
Variational optimization with infinite projected entangled-pair states
Corboz, Philippe
2016-07-01
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states, a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local Hamiltonian. The method is based on a systematic summation of Hamiltonian contributions using the corner-transfer-matrix method. Benchmark results for challenging problems are presented, including the two-dimensional Heisenberg model, the Shastry-Sutherland model, and the t -J model, which show that the variational scheme yields considerably more accurate results than the previously best imaginary-time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.
Adesso, Gerardo; Illuminati, Fabrizio [Dipartimento di Fisica ' E R Caianiello' , Universita degli Studi di Salerno (Italy); CNISM and CNR-Coherentia, Gruppo di Salerno (Italy); and INFN Sezione di Napoli-Gruppo Collegato di Salerno (Italy); Via S Allende, 84081 Baronissi, SA (Italy)
2006-01-15
For continuous-variable (CV) systems, we introduce a measure of entanglement, the CV tangle (contangle), with the purpose of quantifying the distributed (shared) entanglement in multimode, multipartite Gaussian states. This is achieved by a proper convex-roof extension of the squared logarithmic negativity. We prove that the contangle satisfies the Coffman-Kundu-Wootters monogamy inequality in all three-mode Gaussian states, and in all fully symmetric N-mode Gaussian states, for arbitrary N. For three-mode pure states, we prove that the residual entanglement is a genuine tripartite entanglement monotone under Gaussian local operations and classical communication. We show that pure, symmetric three-mode Gaussian states allow a promiscuous entanglement sharing, having both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. These states are thus simultaneous CV analogues of both the GHZ and the W states of three qubits: in CV systems monogamy does not prevent promiscuity, and the inequivalence between different classes of maximally entangled states, holding for systems of three or more qubits, is removed.
Generation of Maximally Entangled Bell State in a Coupled Quantum Dot
ZHANG Ping; FAN Wen-Bin; DUAN Su-Qing; ZHAO Xian-Geng
2001-01-01
We show how the two interacting electrons in a field-driven coupled quantum dot can be used to prepare maximally entangled Bell states. The time durations of the oscillatory electric field for producing and maintaining such highly entangled states are identified by both analytic and exact numerical solutions of the quantum dynamical equations.
Generating multi-mode entangled coherent W and GHZ states via optical system based fusion mechanism
Zang, Xue-Ping; Yang, Ming; Wu, Wei-Feng; Fan, Hong-Yi
2017-05-01
Fusion technology has been demonstrated to be a good method for generating a large-scale entangled coherent W or GHZ state from two small ones in QED system. It is of importance to study how to fuse small-scale entangled coherent W or GHZ states via optical system. In this paper, we present a scheme for generating larger entangled coherent W or GHZ state in an optical system by virtue of fusion technology. The key fusion mechanism is realized by photon detectors and a Mach-Zehnder interferometer with its two arms immersed in Kerr media, by which an n-mode entangled coherent W state and an m-mode entangled coherent W state can be probabilistically fused into an (n+m-2)-mode entangled coherent W state. This fusion scheme applies to entangled coherent GHZ state too but with a unit probability of success. Feasibility analysis indicates that our fusion scheme may be realized with current experimental technology. Large-scale entangled coherent W and GHZ states may find new applications in quantum communication.
Vacuum fluctuations and radiation reaction in radiative processes of entangled states
Menezes, G
2015-01-01
We investigate radiative processes of inertial two-level atoms in an entangled state interacting with a quantum electromagnetic field. We assume a dipole interaction between the atoms. The main intention is to identify and to analyze quantitatively the distinct contributions of vacuum fluctuations and radiation reaction to the decay rate of the entangled state.
Generation of Entangled States of Multiple Superconducting Quantum Interference Devices in Cavity
无
2006-01-01
We propose a scheme for generating the maximally entangled states of many superconducting quantum interference devices (SQUIDs) by using a quantized cavity field and classicalmicrowave pulses in cavity. In the scheme,the maximally entangled states can be generated without requiring the measurement and individual addressing of the SQUIDs.
Scheme for teleportation of unknown single qubit state via continuous variables entangling channel
Wang Zhong-Jie; Zhang Kan; Fan Chao-Yang
2010-01-01
A new scheme for quantum teleportation of single quantum bit state with using continuous variables entangling channel is presented. In our scheme two entangled light fields are employed. An outstanding characteristic of this scheme is that one atomic state is transmitted directly to another atom without using the third atom as the mediate.
Highly enhanced steady-state optomechanical entanglement via cross-Kerr nonlinearity
Chakraborty, Subhadeep
2016-01-01
We study steady-state optomechanical entanglement in presence of an additional cross-Kerr coupling between the optical and mechanical mode. We find that a significant enhancement of the steady-state entanglement can be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature.
Kunkri, Samir; Choudhary, Sujit K.; Ahanj, Ali; Joag, Pramod
2006-02-01
Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy’s nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy’s argument.
FAN Hong-Yi; WANG Yong
2006-01-01
In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.
Bounds on entanglement in qudit subsystems
Kendon, Vivien M.; Zyczkowski, Karol; Munro, William J.
2002-01-01
The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other N-m qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than N/3 qudits will have a positive partial transpose and hence are separable or bound entangled. ...
Entanglement production in Quantized Chaotic Systems
Bandyopadhyay, J N; Bandyopadhyay, Jayendra N.; Lakshminarayan, Arul
2005-01-01
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, presence of chaos in the system produces more entanglement. However, coupling strength between two subsystems is also very important parameter for the entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed state entanglement production...
Quantitative two-qutrit entanglement
Eltschka, Christopher [Institut fuer Theoretische Physik, Universitaet Regensburg, D-93040 Regensburg (Germany); Siewert, Jens [Departamento de Quimica Fisica, Universidad del Pais Vasco UPV/EHU, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, 48011 Bilbao (Spain)
2013-07-01
We introduce the new concept of axisymmetric bipartite states. For d x d-dimensional systems these states form a two-parameter family of nontrivial mixed states that include the isotropic states. We present exact quantitative results for class-specific entanglement as well as for the negativity and I-concurrence of two-qutrit axisymmetric states. These results have interesting applications such as for quantitative witnesses of class-specific entanglement in arbitrary two-qutrit states and as device-independent witness for the number of entangled dimensions.
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-10-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a , uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.
Gaussian Intrinsic Entanglement
Mišta, Ladislav; Tatham, Richard
2016-12-01
We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.
Entanglement in Anderson Nanoclusters
Samuelsson, Peter
2007-01-01
We investigate the two-particle spin entanglement in magnetic nanoclusters described by the periodic Anderson model. An entanglement phase diagram is obtained, providing a novel perspective on a central property of magnetic nanoclusters, namely the temperature dependent competition between local Kondo screening and nonlocal Ruderman-Kittel-Kasuya-Yoshida spin ordering. We find that multiparticle entangled states are present for finite magnetic field as well as in the mixed valence regime and away from half filling. Our results emphasize the role of charge fluctuations.
Joo, Jaewoo; Ginossar, Eran
2016-06-01
We propose a deterministic scheme for teleporting an unknown qubit state through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a microwave photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states transfers a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. In order to facilitate the implementation of such complex protocols we propose a design for reducing the self-Kerr nonlinearity in the cavity. The teleporation scheme enables quantum information processing operations with circuit-QED based on entangled coherent states. These include state verification and single-qubit operations with entangled coherent states. These are shown to be experimentally feasible with the state of the art superconducting circuits.
Joo, Jaewoo; Ginossar, Eran
2016-06-01
We propose a deterministic scheme for teleporting an unknown qubit state through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a microwave photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states transfers a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. In order to facilitate the implementation of such complex protocols we propose a design for reducing the self-Kerr nonlinearity in the cavity. The teleporation scheme enables quantum information processing operations with circuit-QED based on entangled coherent states. These include state verification and single-qubit operations with entangled coherent states. These are shown to be experimentally feasible with the state of the art superconducting circuits.
Lower Bound for entanglement cost of antisymmetric states
Shimono, T
2002-01-01
This report gives a lower bound of entanglement cost for antisymmetric states of bipartite d-level systems to be log_2 (d/(d-1)) ebit (for d=3, E_c >= 0.585...). The paper quant-ph/0112131 claims that the value is equal to one ebit for d=3, since all of the eigenvalues of reduced matrix of any pure states living in N times tensor product of antisymmetric space is not greater than 2^(-N) thus the von Neumann entropy is not less than N, but the proof is not true. Hence whether the value is equal to or less than one ebit is not clear at this moment.
Quantum memory for entangled two-mode squeezed states
Jensen, K; Krauter, H; Fernholz, T; Nielsen, B M; Serafini, A; Owari, M; Plenio, M B; Wolf, M M; Polzik, E S
2010-01-01
A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are (i) versatility (allowing a wide range of inputs) and (ii) true quantum coherence (preserving quantum information). Here we demonstrate such a quantum memory for states possessing Einstein-Podolsky-Rosen (EPR) entanglement. These multi-photon states are two-mode squeezed by 6.0 dB with a variable orientation of squeezing and displaced by a few vacuum units. This range encompasses typical input alphabets for a continuous variable quantum information protocol. The memory consists of two cells, one for each mode, filled with cesium atoms at room temperature with a memory time of about 1msec. The preservation of quantum coherence is rigorously proven by showing that the experimental memory fidelity 0.52(2) significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements.
Gómez, Angela Viviana; Rodríguez, Ferney Javier; Quiroga, Luis; García-Ripoll, Juan José
2016-06-01
Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two-qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Decoherence thermal effects on the entanglement transfer are also discussed. Our results provide evidence that this entanglement transfer by dissipation is feasible, yielding to a steady-state amount of entanglement in the bipartite quantum system which can be optimized for a wide range of realistic physical systems that include state-of-the-art experiments with nitrogen-vacancy centers in diamond, superconducting qubits, or even magnetic molecules embedded in a crystalline matrix.
Synthesizing arbitrary two-photon polarization mixed states
Wei, T C; Branning, D; Goldbart, P M; James, D F V; Jeffrey, E; Kwiat, P G; Mukhopadhyay, S; Peters, N A; Wei, Tzu-Chieh; Altepeter, Joseph B.; Branning, David; Goldbart, Paul M.; Jeffrey, Evan; Kwiat, Paul G.; Mukhopadhyay, Swagatam; Peters, Nicholas A.
2005-01-01
Two methods for creating arbitrary two-photon polarization pure states are introduced. Based on these, four schemes for creating two-photon polarization mixed states are proposed and analyzed. The first two schemes can synthesize completely arbitrary two-qubit mixed states, i.e., control all 15 free parameters: Scheme I requires several sets of crystals, while Scheme II requires only a single set, but relies on decohering the pump beam. Additionally, we describe two further schemes which are much easier to implement. Although the total capability of these is still being studied, we show that they can synthesize all two-qubit Werner states, maximally entangled mixed states, Collins-Gisin states, and arbitrary Bell-diagonal states.
High-concurrence steady-state entanglement of two hole spins in a quantum dot molecular
Yang, Song; Li, ChuanFeng; Zou, XuBo; Guo, GuangCan
2009-01-01
Entanglement, a non-trivial phenomena manifested in composite quantum system, can be served as a new type of physical resource in the emerging technology of quantum information and quantum computation. However, a quantum entanglement is fragile to the environmental-induced decoherence. Here, we present a novel way to prepare a high-concurrence steady-state entanglement of two hole spins in a quantum dot molecular via optical pumping of trion levels. In this scheme, the spontaneous dispassion is used to induce and stabilize the entanglement with rapid rate. It is firstly shown that under certain conditions, two-qubit singlet state can be generated without requiring the state initialization. Then we study the effect of acoustic phonons and electron tunnelings on the scheme, and show that the concurrence of entangled state can be over 0.95 at temperature $T = 1 $K.
戴宏毅; 李承祖; 陈平行
2003-01-01
We present a scheme to probabilistically teleport an arbitrary and unknown three-particle state via a two-particle non-maximally entangled state and a four-particle non-maximally entangled state as the quantum channel. With the help of Bell-state measurements, an arbitrary three-particle state can be perfectly teleported if a receiver introduces a collective unitary transformation. All kinds of unitary transformations are given in greater detail. This scheme can be generalized to the teleportation of an arbitrary and unknown multiparticle state.
Entanglement and photon statistics of output fields from beam splitter for binomial state inputs
Zhou Qing-Ping; Fang Mao-Fa
2004-01-01
The entanglement properties are investigated based on linear entropy, and nonclassicalities are examined of output fields from a beam splitter for pure binomial state inputs. It is shown that the properties of the entanglement and the photon statistics of output fields are not only strongly dependent on the parameters of input binomial states but also quite involved with the nature of the beam splitter. The best entanglement can be obtained when the parameters of both input states and the beam splitter are chosen appropriately. Finally, we analyse briefly the distinguishability between the joint input state and the joint output state.
Tang Jing-Wu; Zhao Guan-Xiang; He Xiong-Hui
2011-01-01
Recently, Peng et al. [2010 Eur. Phys. J. D 58 403] proposed to teleport an arbitrary two-qubit state with a family of four-qubit entangled states, which simultaneously include the tensor product of two Bell states, linear cluster state and Dicke-class state. This paper proposes to implement their scheme in cavity quantum electrodynamics and then presents a new family of four-qubit entangled state |Ω4)1234. It simultaneously includes all the well-known four-qubit entangled states which can be used to teleport an arbitrary two-qubit state. The distinct advantage of the scheme is that it only needs a single setup to prepare the whole family of four-qubit entangled states, which will be very convenient for experimental realization. After discussing the experimental condition in detail, we show the scheme may be feasible based on present technology in cavity quantum electrodynamics.
Optically Excited Entangled States in Organic Molecules Illuminate the Dark.
Upton, L; Harpham, M; Suzer, O; Richter, M; Mukamel, S; Goodson, T
2013-06-20
We utilize quantum entangled photons to carry out nonlinear optical spectroscopy in organic molecules with an extremely small number of photons. For the first time, fluorescence is reported as a result of entangled photon absorption in organic nonlinear optical molecules. Selectivity of the entangled photon absorption process is also observed and a theoretical model of this process is provided. Through these experiments and theoretical modeling it is found that while some molecules may not have strong classical nonlinear optical properties due to their excitation pathways; these same excitation pathways may enhance the entangled photon processes. It is found that the opposite is also true. Some materials with weak classical nonlinear optical effects may exhibit strong non-classical nonlinear optical effects. Our entangled photon fluorescence results provide the first steps in realizing and demonstrating the viability of entangled two-photon microscopy, remote sensing, and optical communications.
Du, Fang-Fang; Long, Gui-Lu
2017-01-01
We present a refined entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled four-electron-spin cluster state by exploring the optical selection rules derived from the quantum-dot spins in one-sided optical microcavities. In our ECP, the parties obtain not only the four-electron-spin systems in the partial entanglement with two unknown parameters, but also the less-entangled two-electron-spin systems in the first step. Utilizing the above preserved systems as the resource for the second step of our ECP, the parties can obtain a standard cluster state by keeping the robust odd-parity instances with two parity-check gates. Meanwhile, the systems in the rest three instances can be used as the resource in the next round of our ECP. The success probability of our ECP is largely increased by iteration of the ECP process. Moreover, all the coefficients of our ECP are unknown for the parties without assistance of extra single electron-spin, so our ECP maybe has good applications in quantum communication network in the future.
Thomas rotation and the mixed state geometric phase
Levay, Peter [Department of Theoretical Physics, Institute of Physics, Technical University of Budapest, H-1521 Budapest (Hungary)
2004-04-23
It is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by 2 x 2 density matrices is just the path-ordered product of Thomas rotations. These rotations are invariant under hyperbolic translations inside the Bloch sphere that can be regarded as the Poincare ball model of hyperbolic geometry. A general expression for the mixed state geometric phase for an arbitrary geodesic triangle in terms of the Bures fidelities is derived. The formula gives back the solid angle result well known from studies of the pure state geometric phase. It is also shown that this mixed state anholonomy can be reinterpreted as the pure state non-Abelian anholonomy of entangled states living in a suitable restriction of the quaternionic Hopf bundle. In this picture Uhlmann's parallel transport is just the Pancharatnam transport of quaternionic spinors.
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.
Sustainable Entangled State of Two Qutrits Under Laser Irradiation
Biryukov A.А.
2015-01-01
Full Text Available We study the evolution of quantum entanglement in the model of two identical qubits interacting with a single-mode laser field. The density matrix and Peres-Horodecki parameter are calculated within the frameworks of path-integral formalism. The quantum entanglement measure is shown to be strongly dependent upon the phase difference between the laser radiation acting on each cubit. This observation may offer the possibility of quantum entanglement stationary control by varying the distance between the qubits.
Cao, Cong; Fan, Ling; Chen, Xi; Duan, Yu-Wen; Wang, Tie-Jun; Zhang, Ru; Wang, Chuan
2017-04-01
We propose an efficient entanglement concentration protocol (ECP) for nonlocal three-atom systems in an arbitrary unknown less-entangled W state, resorting to the Faraday rotation of photonic polarization in cavity quantum electrodynamics and the systematic concentration method. In the first step of the present ECP, one party in quantum communication performs a parity-check measurement on her two atoms in two three-atom systems for dividing the composite six-atom systems into two groups. In the first group, the three parties will obtain some three-atom systems in a less-entangled state with two unknown coefficients. In the second group, they will obtain some less-entangled two-atom systems. In the second step of the ECP, the three parties can obtain a subset of three-atom systems in the standard maximally entangled W state by exploiting the above three-atom and two-atom systems. Moreover, the preserved systems in the failed instances can be used as the resource for the entanglement concentration in the next round. The total success probability of the ECP can therefore be largely increased by iterating the entanglement concentration process several rounds. The distinct feature of our ECP is that we can concentrate arbitrary unknown atomic entangled W states via photonic Faraday rotation, and thus it may be universal and useful for entanglement concentration in future quantum communication network.
Sang, Zhi-wen
2017-07-01
We demonstrate that a seven-particle entangled state can be used to realize the deterministic asymmetric bidirectional controlled remote state preparation. That is to say Alice can remotely prepare an arbitrary known single-particle state for Bob and at the same time Bob can remotely prepare an arbitrary known two-particle state for Alice with the help of the supervisor Charlie. In our scheme, only single-particle projective measurements and two-particle projective measurement are needed.
An entanglement concentration protocol for cluster states using CNOT gate operation
CHOUDHURY BINAYAK S; DHARA ARPAN
2016-05-01
The purpose of this paper is a proposal on entanglement concentration protocol forcluster states. The protocol uses CNOT gate operation and is assisted with a single qubit. Moreover, the local and non-local operations are performed by a single party. We also make a comparative numerical study of the residual entanglement left out after the execution of each step of the protocol.
Observables Can Be Tailored to Make Any Pure State Entangled (or Not)
Harshman, N L
2011-01-01
We show that for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured d-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.
Observables can be tailored to change the entanglement of any pure state
Harshman, N. L. [Department of Physics, American University, 4400 Massachusetts Ave., NW, Washington, DC 20016-8058 (United States); Ranade, Kedar S. [Institut fuer Quantenphysik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89081 Ulm (Germany)
2011-07-15
We show that, for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured d-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that, in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.
A Criterion for Maximally Six-Qubit Entangled States via Coefficient Matrix
Yu, Yan; Zha, Xin Wei; Li, Wei
2017-03-01
In a recent paper (J. Phys. A: Math. Theor 45, 075308 (2012)), Li et al. established the coefficient matrix of six-qubit entangled states. With an emphasis on six qubits, we present a new criterion for maximally six-qubit entangled states via those coefficient matrices. By calculating the determinants of coefficient matrix, one use the criterion that characterize these states. Moreover, the criterion via the coefficient matrices gives rise to the combination of maximally multi-qubit entangled state(MMES) and matrix, and we believe that the new criterion can play an important role in quantum information.
Dynamics of a multi-mode maximum entangled coherent state over an amplitude damping channel
A. E1 Allati; Y. Hassouni; N. Metwally
2011-01-01
The dynamics of the maximum entangled coherent state traveling through an amplitude damping channel is investigated.For small values of the transmissivity rate,the traveling state is very fragile to this noise channel,which suffers from the phase flip error with high probability. The entanglement decays smoothly for larger values of the transmissivity rate and speedily for smaller values of this rate.As the number of modes increases,the traveling state over this noise channel quickly loses its entanglement.The odd and even states vanish at the same value of field intensity.
Dynamics of multi-modes maximum entangled coherent state over amplitude damping channel
Allati, A El; Metwally, N
2012-01-01
The dynamics of maximum entangled coherent state travels through an amplitude damping channel is investigated. For small values of the transmissivity rate the travelling state is very fragile to this noise channel, where it suffers from the phase flip error with high probability. The entanglement decays smoothly for larger values of the transmissivity rate and speedily for smaller values of this rate. As the number of modes increases, the travelling state over this noise channel loses its entanglement hastily. The odd and even states vanish at the same value of the field intensity.
Quantum entanglement and quantum operation
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.
A Scheme for Atomic Entangled States and Quantum Gate Operations in Cavity QED
LI Peng-Bo; GU Ying; GONG Qi-Huang; GUO Guang-Can
2009-01-01
We propose a scheme for controllably entangling the ground states of five-state W-type atoms confined in a cavity and realizing swap gate and phase gate operations.In this scheme the cavity is only virtually excited and the atomic excited states are almost not occupied,so the produced entangled states and quantum logic operations are very robust against the cavity decay and atomic spontaneous emission.
Generation of Entangled Coherent States in Raman-Coupled Bose-Einstein Condensates
KUANG Le-Man; ZENG Ai-Hua; KUANG Zhen-Hua
2004-01-01
A method for producing entangled coherent states (ECSs) for atomic Bose-Einstein condensates (BECs) is presented. The proposed method involves a BEC with three internal states and two classical laser beams in a three-level Lambda configuration. We show how to generate multi-state ECSs through properly manipulating strengths of these interactions and laser detunings. A maximally entangled coherent state is obtained explicitly.
无
2007-01-01
We present two schemes for concentrating unknown nonmaximally entangled Greenberger-Horme-Zeilinger (GHZ) or W class states. The first scheme for concentrating the nonmaximally entangled GHZ state is based on linear optical devices. The second scheme for concentrating the W class states can be applied to a wide variety of atomic state.Both of our schemes are not postselection ones and are within the current technologies.
Experimental generation of complex noisy photonic entanglement
Dobek, K; Demkowicz-Dobrzanski, R; Banaszek, K; Horodecki, P
2011-01-01
We describe an experimental setup based on spontaneous parametric down-conversion to produce multiple photon pairs in maximally entangled polarization states using an arrangement of two type-I nonlinear crystals. By introducing correlated polarization noise in the paths of the generated photons one can prepare mixed entangled states whose properties illustrate fundamental results obtained recently in quantum information theory, in particular those concerning bound entanglement and privacy.
Wang, Dong; Hoehn, Ross D.; Ye, Liu; Kais, Sabre
2016-07-01
We present a strategy for realizing multiparty-controlled remote state preparation (MCRSP) for a family of four-qubit cluster-type states by taking a pair of partial entanglements as the quantum channels. In this scenario, the encoded information is transmitted from the sender to a spatially separated receiver with control of the transmission by multiple parties. Predicated on the collaboration of all participants, the desired state can be faithfully restored at the receiver's location with high success probability by application of additional appropriate local operations and necessary classical communication. Moreover, this proposal for MCRSP can be faithfully achieved with unit total success probability when the quantum channels are distilled to maximally entangled ones.
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems
Ghader Najarbashi
2011-01-01
Full Text Available In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs described by Grassmann numbers for n>2 degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some well-known entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor product of GCSs. It is shown that for three level systems, the Grassmann creation and annihilation operators b and b^† together with bz form a closed deformed algebra, i.e., SU_q(2 with q=e^{2πi/3}, which is useful to construct entangled qutrit-states. The same argument holds for three level squeezed states. Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled super coherent states.
Induced measures in the space of mixed quantum states
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warsaw, Poland and Instytut Fizyki, Uniwersytet Jagiellonski, Crakow (Poland)). E-mail: karol@cft.edu.pl; Sommers, Hans-Juergen [Fachbereich Physik, Universitaet-Gesamthochschule Essen, Essen (Germany)). E-mail: sommers@next30.theo-phys.uni-essen.de
2001-09-07
We analyse several product measures in the space of mixed quantum states. In particular, we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a NxK composite system, induces a unique measure in the space of NxN mixed states (or in the space of KxK mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of NxN pure states behaves as lnN-1/2. (author)
Induced measures in the space of mixed quantum states
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
2001-01-01
We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K composite system, induces a unique measure in the space of N x N mixed states (or in the space of K x K mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of $N \\times N$ pure states behaves as lnN-1/2.
Generation and application of a controllable multi-atom entangled state
Huang Yan-Xia; Zhan Ming-Sheng
2004-01-01
In this paper, we present a scheme to prepare a set of the multi-atom entangled states by the cavity quantum electrodynamics (QED) technology. The multi-atom entangled states have some particular entanglement properties.For example, the remaining reduced density matrices Pij still retain entanglement or disentanglement when any N-2atoms of the N atoms are traced out, which can be chosen freely according to our need, and the relative entanglement strength of any pair of atoms (measured by the concurrence) can be arbitrarily adjusted. In addition, they may be completely symmetric under the exchange of any two atoms, and perform certain quantum information tasks, such as telecloning, teleportation, secret sharing and so on.
Generation and application of a controllable multi-atom entangled state
Huang, Yan-Xia; Zhan, Ming-Sheng
2004-12-01
In this paper, we present a scheme to prepare a set of the multi-atom entangled states by the cavity quantum electrodynamics (QED) technology. The multi-atom entangled states have some particular entanglement properties. For example, the remaining reduced density matrices ρij still retain entanglement or disentanglement when any N-2 atoms of the N atoms are traced out, which can be chosen freely according to our need and the relative entanglement strength of any pair of atoms (measured by the concurrence) can be arbitrarily adjusted. In addition, they may be completely symmetric under the exchange of any two atoms and perform certain quantum information tasks, such as telecloning, teleportation, secret sharing and so on.
Random pure states: Quantifying bipartite entanglement beyond the linear statistics.
Vivo, Pierpaolo; Pato, Mauricio P; Oshanin, Gleb
2016-05-01
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite N,M. Then, we focus on the moments E{K^{a}} of the Schmidt number K, the reciprocal of the purity. This is a random variable supported on [1,N], which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for E{K^{a}} for N=2 and 3 and arbitrary M, and also for square N=M systems by spotting for the latter a connection with the probability P(x_{min}^{GUE}≥sqrt[2N]ξ) that the smallest eigenvalue x_{min}^{GUE} of an N×N matrix belonging to the Gaussian unitary ensemble is larger than sqrt[2N]ξ. As a by-product, we present an exact asymptotic expansion for P(x_{min}^{GUE}≥sqrt[2N]ξ) for finite N as ξ→∞. Our results are corroborated by numerical simulations whenever possible, with excellent agreement.
Random pure states: Quantifying bipartite entanglement beyond the linear statistics
Vivo, Pierpaolo; Pato, Mauricio P.; Oshanin, Gleb
2016-05-01
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M . Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N ≤M , a general relation between the n -point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite N ,M . Then, we focus on the moments E {Ka} of the Schmidt number K , the reciprocal of the purity. This is a random variable supported on [1 ,N ] , which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for E {Ka} for N =2 and 3 and arbitrary M , and also for square N =M systems by spotting for the latter a connection with the probability P (xminGUE≥√{2 N }ξ ) that the smallest eigenvalue xminGUE of an N ×N matrix belonging to the Gaussian unitary ensemble is larger than √{2 N }ξ . As a by-product, we present an exact asymptotic expansion for P (xminGUE≥√{2 N }ξ ) for finite N as ξ →∞ . Our results are corroborated by numerical simulations whenever possible, with excellent agreement.
Continuous variable entanglement distillation of non-Gaussian states
Lassen, Mikael Østergaard; Dong, Ruifang; Heersink, Joel
2009-01-01
We experimentally demonstrate distillation of continuous variable entangled light that has undergone non-Gaussian attenuation loss. The continuous variable entanglement is generated with optical fibers and sent through a lossy channel, where the transmission is varying in time. By employing simple...
Entanglement of remote transmon qubits by concurrent measurement using Fock states
Narla, A.; Hatridge, M.; Shankar, S.; Leghtas, Z.; Sliwa, K. M.; Vlastakis, B.; Zalys-Geller, E.; Mirrahimi, M.; Devoret, M. H.
2015-03-01
A requirement of any modular quantum computer is the ability to maintain individual qubits in isolated environments while also being able to entangle arbitrary distant qubits on demand. For superconducting qubits, such a protocol can be realized by first entangling the qubits with flying microwave coherent states which are then concurrently detected by a parametric amplifier. This protocol has a 50% success probability but is vulnerable to losses between the qubits and the amplifier which reduce the entanglement fidelity. An alternative is to use itinerant Fock states, since losses now tend to reduce the success probability of creating an entangled state but not its fidelity. Such single-photon protocols have been implemented in trapped-ion and NV-center experiments. We present such a protocol tailored for entangling two transmon qubits in the circuit QED architecture. Each qubit is entangled with a Fock state of its cavity using sideband pulses. The Fock states leak out of the cavity, interfere on a beam-splitter which erases their which-path information, and are subsequently detected using a novel photo-detector realized by another qubit-cavity system. Simulations suggest that we can realize a high-fidelity entangled state with a success probability as large as 1%.
Robust generation of high-fidelity entangled states for multiple atoms
Lin Li-Hua
2009-01-01
A scheme is presented for generating entangled states of multiple atoms in a cavity. In the scheme the atoms simultaneously interact with a cavity mode, with the first atom driven by two classical fields and the other atoms driven by a classical field. Our scheme is valid even if the cavity decay rate is larger than the effective coupling strength, which is important for experiment. The generation of entangled states is conditional on the detection of a photon decaying from the cavity and thus the fidelity of the entangled state is insensitive to the detection inefficiency. Furthermore, the scheme can be applied to the case with any number of atoms in principle.
Teleportation of an arbitrary unknown N-qubit entangled state under the controlling of M controllers
LIU Yu-ling; MAN Zhong-xiao; XIA Yun-jie
2008-01-01
A new quantum protocol to teleport an arbitrary unknown N-qubit entangled state from a sender to a fixed receiver under M controllers(M < N) is proposed. The quantum resources required are M non-maximally entangled Greenberger-Home-Zeilinger (GHZ) state and N-M non-maximally entangled Einstein-Podolsky-Rosen (EPR) pairs. The sender performs N generalized Bell-state measurements on the 2N particles. Controllers take M single-particle measurement along x-axis, and the receiver needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if controllers cooperate with it.
Schemes for Probabilistic Teleportation of an Unknown Three-Particle Three-Level Entangled State
无
2006-01-01
In this paper, two schemes for teleporting an unknown three-particle three-level entangled state are proposed. In the first scheme, two partial three-particle three-level entangled states are used as the quantum channels, while in the second scheme, three two-particle three-level non-maximally entangled states are employed as quantum channels.It is shown that the teleportation can be successfully realized with certain probability, for both two schemes, if a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.
Two-photon path-entangled states in multi-mode waveguides
Poem, Eilon; Silberberg, Yaron
2012-01-01
We experimentally show that two-photon path-entangled states can be coherently manipulated by multi-mode interference in multi-mode waveguides. By measuring the output two-photon spatial correlation function versus the phase of the input state, we show that multi-mode waveguides perform as nearly-ideal multi-port beam splitters at the quantum level, creating a large variety of entangled and separable multi-path two-photon states.
Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit Entangled State
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.
Quantum Entanglement and Teleportation of Quantum-Dot States in Microcavities
Miranowicz, A; Liu, Yu-xi; Chimczak, G; Koashi, M; Imoto, N; 10.1380/ejssnt.2007.51
2009-01-01
Generation and control of quantum entanglement are studied in an equivalent-neighbor system of spatially-separated semiconductor quantum dots coupled by a single-mode cavity field. Generation of genuinely multipartite entanglement of qubit states realized by conduction-band electron-spin states in quantum dots is discussed. A protocol for quantum teleportation of electron-spin states via cavity decay is briefly described.
Barium Qubit State Detection and Ba Ion-Photon Entanglement
Sosnova, Ksenia; Inlek, Ismail Volkan; Crocker, Clayton; Lichtman, Martin; Monroe, Christopher
2016-05-01
A modular ion-trap network is a promising framework for scalable quantum-computational devices. In this architecture, different ion-trap modules are connected via photonic buses while within one module ions interact locally via phonons. To eliminate cross-talk between photonic-link qubits and memory qubits, we use different atomic species for quantum information storage (171 Yb+) and intermodular communication (138 Ba+). Conventional deterministic Zeeman-qubit state detection schemes require additional stabilized narrow-linewidth lasers. Instead, we perform fast probabilistic state detection utilizing efficient detectors and high-NA lenses to detect emitted photons from circularly polarized 493 nm laser excitation. Our method is not susceptible to intensity and frequency noise, and we show single-shot detection efficiency of ~ 2%, meaning that we can discriminate between the two qubits states with 99% confidence after as little as 50 ms of averaging. Using this measurement technique, we report entanglement between a single 138 Ba+ ion and its emitted photon with 86% fidelity. This work is supported by the ARO with funding from the IARPA MQCO program, the DARPA Quiness program, the AFOSR MURI on Quantum Transduction, and the ARL Center for Distributed Quantum Information.
Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states
Wang, Xin-Wen; Tang, Shi-Qing; Yuan, Ji-Bing; Zhang, Deng-Yu
2017-06-01
It has been shown that a nearly pure Greenberger-Horne-Zeilinger (GHZ) state could be distilled from a large (even infinite) number of GHZ-diagonal states that can be obtained by depolarizing general multipartite mixed states (non-GHZ-diagonal states) through sequences of (probabilistic) local operations and classical communications. We here demonstrate that perfect GHZ states can be extracted, with certain probabilities, from two copies of non-GHZ-diagonal mixed states when some conditions are satisfied. This result implies that it is not necessary to depolarize these entangled mixed states to the GHZ-diagonal type, and that they are better than GHZ-diagonal states for distillation of pure GHZ states. We find a wide class of multipartite entangled mixed states that fulfill the requirements. Moreover, we display that the obtained result can be applied to practical noisy environments, e.g., amplitude-damping channels. Our findings provide an important complementarity to conventional GHZ-state distillation protocols (designed for GHZ-diagonal states) in theory, as well as having practical applications.
Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
Fan, Zheyong; Goertzel, Ben; Ren, Zhongzhou; Zeng, Huabi
2010-01-01
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found.
Carving complex many-atom entangled states by single-photon detection
Chen, Wenlan; Duan, Yiheng; Braverman, Boris; Zhang, Hao; Vuletic, Vladan
2015-01-01
We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multi-frequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. Complex entangled states such as multicomponent Schroedinger cat states can be generated with high fidelity. This probabilistic but fast heralded state-carving method can be made quasi-deterministic by repeated trial and feedback, yields high success probability per trial, and can be implemented with existing technology.
MEI Yu-Xue; CHEN Lin; CHEN Yi-Xin
2006-01-01
@@ In a process of remote state preparation, the universality of quantum channel is an essential ingredient. That is, one quantum channel should be feasible to remotely prepare any given qubit state. This problem appears in a process where one uses non-maximally entangled state as the passage. We present a scheme in which any given qubit |φ〉 = cosθ|0〉 + sinθeiψ|1〉 could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled state with a high fidelity, under the condition that the receiver holds the knowledge of θ. This condition is helpful to reduce the necessary amount of quantum channels, which is proven to be a low quantity to realize the universality. We also give several methods to investigate the trade-off between this amount and the achievable fidelity of the protocol.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Asymmetric Controlled Bidirectional Remote State Preparation by Using a Ten-qubit Entangled State
Ma, Peng-Cheng; Chen, Gui-Bin; Li, Xiao-Wei; Zhang, Jian; Zhan, You-Bang
2017-09-01
We present a novel scheme for asymmetric controlled bidirectional remote state preparation (ACBRSP) with complex coefficients via a ten-qubit entangled state as the quantum channel. In this scheme, two distant parties, Alice and Bob are not only senders but also receivers, and Alice wants to remotely prepare a single-qubit state at Bob's site, at the same time, Bob wishes to help Alice remotely prepares an arbitrary two-qubit entangled state. It is shown that, only if the two senders and the controller collaborate with each other, the ACBRSP can be completed successfully. We demonstrate that the total success probability of the ACBRSP in this scheme can reach 1, that is, the scheme is deterministic.
Benchmarks and statistics of entanglement dynamics
Tiersch, Markus
2009-09-04
In the present thesis we investigate how the quantum entanglement of multicomponent systems evolves under realistic conditions. More specifically, we focus on open quantum systems coupled to the (uncontrolled) degrees of freedom of an environment. We identify key quantities that describe the entanglement dynamics, and provide efficient tools for its calculation. For quantum systems of high dimension, entanglement dynamics can be characterized with high precision. In the first part of this work, we derive evolution equations for entanglement. These formulas determine the entanglement after a given time in terms of a product of two distinct quantities: the initial amount of entanglement and a factor that merely contains the parameters that characterize the dynamics. The latter is given by the entanglement evolution of an initially maximally entangled state. A maximally entangled state thus benchmarks the dynamics, and hence allows for the immediate calculation or - under more general conditions - estimation of the change in entanglement. Thereafter, a statistical analysis supports that the derived (in-)equalities describe the entanglement dynamics of the majority of weakly mixed and thus experimentally highly relevant states with high precision. The second part of this work approaches entanglement dynamics from a topological perspective. This allows for a quantitative description with a minimum amount of assumptions about Hilbert space (sub-)structure and environment coupling. In particular, we investigate the limit of increasing system size and density of states, i.e. the macroscopic limit. In this limit, a universal behaviour of entanglement emerges following a ''reference trajectory'', similar to the central role of the entanglement dynamics of a maximally entangled state found in the first part of the present work. (orig.)
Einstein-Podolsky-Rosen Entanglement in a Vacuum-Class Two-Mode Squeezed State
Eberle, Tobias; Duhme, Jörg; Franz, Torsten; Werner, Reinhard F; Schnabel, Roman
2011-01-01
Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low resource generation of bi-partite continuous variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e. the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.3 %. However, arbitrary strong EPR entanglement is generally possible with this scheme. We realize continuous wave squeezed light at 1550 nm with up to 9.9 dB of non-classical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase controlled balanced homodyne detectors we observe an EPR co-variance product of 0.502 \\pm 0.006 < 1, where 1 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.
Scheme for teleportation of entangled states without Bell-state measurement by using one atom
Qiang Wenchao; Zhang Lei; Zhang Aiping [Faculty of Science, Xi' an University of Architecture and Technology, Xi' an 710055 (China); Dong Shihai, E-mail: qwcqj@163.com [Departamento de Fisica, Esc. Sup de Fisica y Matematicas, Instituto Politecnico Nacional, Edificio 9, Unidad Profesional Adolfo Lopez Mateos, Mexico, DF 07738 (Mexico)
2011-07-01
We propose a scheme for approximately and conditionally teleporting an entanglement of zero- and one-photon states from a cavity with left- and right-polarized modes to another similar one, with a fidelity exceeding 99%. Instead of using the Bell-state measurement, only one atom is used in our scheme. The time spent, the success probability and the feasibility of the proposed scheme are also discussed.
无
2009-01-01
The generalized continuous variable two-mode entangled state |〉 is proposed by using the tech-nique of integration within an ordered product (IWOP) of operators. The characteristics of this new entangled representation and its application in quantum teleportation are analyzed in detail. These results indicate that such real parameters |〉 indeed make up a new entangled representation owing to its completeness and orthogonal relation. By employing the |〉 as quantum transmission channel,the teleportation of any single-mode quantum state |ψ〉 3 can be realized by a unitary transformation.
Quantum Cloning of an Unknown 2-Atom State via Entangled Cluster States
Yu, L.-z.; Zhong, F.
2016-06-01
This paper presented a scheme for cloning a 2-atom state in the QED cavity with the help of Victor who is the state's preparer. The cloning scheme has two steps. In the first step, the scheme requires probabilistic teleportation of a 2-atom state that is unknown in advance, and uses a 4-atom cluster state as quantum channel. In the second step, perfect copies of the 2-atom entangled state may be realized with the assistance of Victor. The finding is that our scheme has two outstanding advantages: it is not sensitive to the cavity decay, and Bell state is easy to identify.
Quantum Entanglement Channel based on Excited States in a Spin Chain
张少良; 杜良辉; 郭光灿; 周幸祥; 周正威
2011-01-01
We study the possibility of using a spin chain to construct a quantum entanglement channel that can be used for quantum state transmission in a solid state system.We analyze the spin chain's states under various z-directional magnetic field and spin interactions to determine the entanglement between Alice and Bob's spins.We derive the conditions under which this entanglement can be distilled,and find that a spin chain of arbitrary length can be used as a quantum channel for quantum state transmission when the number of spin flips in the chain is large.%We study the possibility of using a spin chain to construct a quantum entanglement channel that can be used for quantum state transmission in a solid state system. We analyze the spin chain's states under various z-directional magnetic field and spin interactions to determine the entanglement between Alice and Bob's spins. We derive the conditions under which this entanglement can be distilled, and find that a spin chain of arbitrary length can be used as a quantum channel for quantum state transmission when the number of spin Hips in the chain is large.
Popp, M; Martín-Delgado, M A; Cirac, J I
2004-01-01
We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chai...
Entanglement concentration for two-mode Gaussian states in non-inertial frames
Di Noia, Maurizio; Giraldi, Filippo; Petruccione, Francesco
2017-04-01
Entanglement creation and concentration by means of a beam splitter (BS) is analysed for a generic two-mode bipartite Gaussian state in a relativistic framework. The total correlations, the purity and the entanglement in terms of logarithmic negativity are analytically studied for observers in an inertial state and in a non-inertial state of uniform acceleration. The dependence of entanglement on the BS transmissivity due to the Unruh effect is analysed in the case when one or both observers undergo uniform acceleration. Due to the Unruh effect, depending on the initial Gaussian state parameters and observed accelerations, the best condition for entanglement generation limited to the two modes of the observers in their regions is not always a balanced beam splitter, as it is for the inertial case.
A Scheme for Preparation of W-Type Entangled Coherent State of Three-Cavity Fields
YUAN Chun-Hua; OU Yong-Cheng; ZHANG Zhi-Ming
2006-01-01
@@ We present an experimental scheme to prepare the three-cavity W-type entangled coherent state in the context of dispersive cavity quantum electrodynamics. The discussion of our scheme indicates that it can be realized by current technology.
Two Theorems on Calculating the Relative Entropy of Entanglement
WU Sheng-Jun; ZHANG Yong-De; WU Qiang
2001-01-01
We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.
Generation of an Entangled State of Two Multilevel Atoms in Cavity QED
ZHAN Zhi-Ming; YANG Wen-Xing; LI Jia-Hua
2004-01-01
@@ We present a simple scheme to generate a maximally entangled state of two four-level Rydberg atoms with a nonresonant cavity by cavity-assisted collisions. By using this scheme, the maximally entangled state of two N-level (N ＞ 4) Rydberg atoms can also be obtained. During the passage of the atoms through the cavity field,they are only virtually excited. There is no quantum information that will be transferred from the atoms to the cavity in this case.
Arbitrated quantum signature scheme based on χ-type entangled states
Zuo, Huijuan; Huang, Wei; Qin, Sujuan
2013-10-01
An arbitrated quantum signature scheme, which is mainly applied in electronic-payment systems, is proposed and investigated. The χ-type entangled states are used for quantum key distribution and quantum signature in this protocol. Compared with previous quantum signature schemes which also utilize χ-type entangled states, the proposed scheme provides higher efficiency. Finally, we also analyze its security under various kinds of attacks.
EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU（2） Algebra
FANHong-Yi; CHENJun-Hua
2003-01-01
We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation descr/bing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some ttamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.
EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra
FAN Hong-Yi; CHEN Jun-Hua
2003-01-01
We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.
JIANG Nian-Quan
2005-01-01
@@ By extending the Einstein-Podolsky-Rosen (EPR) bipartite entanglement to an n-partite case, we construct the common eigenstate of the n-partite total coordinate and relative momenta for the continuous variables. The entanglement property of the state is shown. The classical dilation transform of variables in such a state induces a new n-mode squeezing operator related to an n-mode bosonic operator realization of SU(1,1) Lie algebra.
Experimental test of local realism using non-maximally entangled states
Genovèse, M; Novero, C; Predazzi, Enrico
2000-01-01
In this paper we describe a test of Bell inequalities using a non- maximally entangled state, which represents an important step in the direction of eliminating the detection loophole. The experiment is based on the creation of a polarisation entangled state via the superposition, by use of an appropriate optics, of the spontaneous fluorescence emitted by two non-linear crystals driven by the same pumping laser.
Preparation of Entangled Atomic States Through Resonant Atom-Field Interaction
无
2006-01-01
A scheme is proposed for the generation of two-atom maximally entangled states and multi-atom maximally entangled states of W class. The scheme is based on the simultaneous resonant interaction of atoms with a single-mode cavity field. It does not require accurate adjustment of the interaction time. The time needed to complete the generation does not increase with the number of the atom.
Probabilistic teleportation scheme of two-mode entangled photon states by using linear optic element
XIANG Shao-hua
2003-01-01
A scheme for teleporting two-mode entangled photon states with the successful probability 33.3% is proposed. In the scheme, the teleporte d qubit is two-mode photon entangled states, and two pairs of EPR pair are used as quantum channel between a sender and a receiver. This procedure is achieved by using two 50/50 symmetric beam splitters and four photon number detectors wit h the help of classical information.
Entanglement production in quantized chaotic systems
Jayendra N Bandyopadhyay; Arul Lakshminarayan
2005-04-01
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, chaos in the system produces more entanglement. However, coupling strength between two subsystems is also a very important parameter for entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed-state entanglement production are qualitatively similar to the pure state entanglement production. We however still lack an analytical understanding of the mixed-state entanglement production in chaotic systems.
Local approach to quantum entanglement
Ho-Chih, Lin
Quantum entanglement is the key property that makes quantum information theory different from its classical counterpart and is also a valuable physical resource with massive potential for technological applications. However, our understanding of entanglement is still far from com plete despite intense research activities. Like other physical resources, the first step towards exploiting them fully is to know how to quantify. There are many reasons to focus on the en tanglement of continuous-variable states since the underlying degrees of freedom of physical systems carrying quantum information are frequently continuous, rather than discrete. Much of the effort has been concentrated on Gaussian states, because these are common as the ground or thermal states of optical modes. Within this framework, many interesting topics have been stud ied and some significant progress made. Nevertheless, non-Gaussian states are also extremely important this is especially so in condensed-phase systems, where harmonic behaviour in any degree of freedom is likely to be only an approximation. So far, there is little knowledge about the quantification of entanglement in non-Gaussian states. This thesis aims to contribute to the active field of research in quantum entanglement by introducing a new approach to the analysis of entanglement, especially in continuous-variable states, and shows that it leads to the first systematic quantification of the (local) entanglement in arbitrary bipartite non-Gaussian states. By applying this local approach, many new insights can be gained. Notably, local entanglements of systems with smooth wavefunctions are fully characterised by the derived simple expressions, provided the wavefunction is known. The local (logarithmic) negativity of any two-mode mixed states can be directly computed from the closed-form formulae given. For multi-mode mixed states, this approach provides a scheme that permits much simpler numerical computation for quantifying
Quantum communication for satellite-to-ground networks with partially entangled states
Chen, Na; Quan, Dong-Xiao; Pei, Chang-Xing; Yang-Hong
2015-02-01
To realize practical wide-area quantum communication, a satellite-to-ground network with partially entangled states is developed in this paper. For efficiency and security reasons, the existing method of quantum communication in distributed wireless quantum networks with partially entangled states cannot be applied directly to the proposed quantum network. Based on this point, an efficient and secure quantum communication scheme with partially entangled states is presented. In our scheme, the source node performs teleportation only after an end-to-end entangled state has been established by entanglement swapping with partially entangled states. Thus, the security of quantum communication is guaranteed. The destination node recovers the transmitted quantum bit with the help of an auxiliary quantum bit and specially defined unitary matrices. Detailed calculations and simulation analyses show that the probability of successfully transferring a quantum bit in the presented scheme is high. In addition, the auxiliary quantum bit provides a heralded mechanism for successful communication. Based on the critical components that are presented in this article an efficient, secure, and practical wide-area quantum communication can be achieved. Project supported by the National Natural Science Foundation of China (Grant Nos. 61072067 and 61372076), the 111 Project (Grant No. B08038), the Fund from the State Key Laboratory of Integrated Services Networks (Grant No. ISN 1001004), and the Fundamental Research Funds for the Central Universities (Grant Nos. K5051301059 and K5051201021).
Generation of entangled states and error protection from adiabatic avoided level crossings
Bell, N F; Volkas, R R; Wong, Y Y Y; Bell, Nicole F.; Volkas, Raymond R.; Wong, Yvonne Y. Y.
2002-01-01
We consider the environment-affected dynamics of $N$ self-interacting particles living in one-dimensional double wells. Two topics are dealt with. First, we consider the production of entangled states of two-level systems. We show that by adiabatically varying the well biases we may dynamically generate maximally entangled states, starting from initially unentangled product states. Entanglement degradation due to a common type of environmental influence is then computed by solving a master equation. However, we also demonstrate that entanglement production is unaffected if the system-environment coupling is of the type that induces ``motional narrowing''. As our second but related topic, we construct a different master equation that seamlessly merges error protection/detection dynamics for quantum information with the environmental couplings responsible for producing the errors in the first place. Adiabatic avoided crossing schemes are used in both topics.
Nonlocal entanglement and noise between spin qubits induced by Majorana bound states
Ke, Sha-Sha [State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Lü, Hai-Feng, E-mail: lvhf81@gmail.com [State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong (China); Yang, Hua-Jun [State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Guo, Yong [Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084 (China); Collaborative Innovation Center of Quantum Matter, Beijing (China); Zhang, Huai-Wu [State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China)
2015-01-23
We propose a scheme to create nonlocal entanglement between two spatially separated electron spin qubits by coupling them with a pair of Majorana bound states (MBSs). The spin qubits are based on the spins of electrons confined in quantum dots. It is shown that spin entanglement between two dots could be generated by the nonlocality of MBSs. We also demonstrate that in the transport regime, the current noise cross correlation can serve as a good indicator of spin entanglement. The Majorana-dot coupling not only induces an indirect interaction between qubits, but also produces spin localization in the strong coupling limit. These two competing effects lead to a nonmonotonic dependence of current cross-correlation and entanglement on the Majorana-qubit coupling strength. - Highlights: • We propose a scheme to create nonlocal entanglement between two spatially separated electron spin qubits by coupling them with a pair of Majorana bound states. • Spin entanglement between two dots could be generated by the nonlocality of MBSs. • The current noise cross correlation can serve as a good indicator of spin entanglement.
Multipartite quantum entanglement evolution in photosynthetic complexes.
Zhu, Jing; Kais, Sabre; Aspuru-Guzik, Alán; Rodriques, Sam; Brock, Ben; Love, Peter J
2012-08-21
We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.
Evolution of Pure States into Mixed States
Liu, J
1993-01-01
In the formulation of Banks, Peskin and Susskind, we show that one can construct evolution equations for the quantum mechanical density matrix $\\rho$ with operators which do not commute with hamiltonian which evolve pure states into mixed states, preserve the normalization and positivity of $\\rho$ and conserve energy. Furthermore, it seems to be different from a quantum mechanical system with random sources.
Entanglement dynamics in the presence of controlled unital noise.
Shaham, A; Halevy, A; Dovrat, L; Megidish, E; Eisenberg, H S
2015-06-10
Quantum entanglement is notorious for being a very fragile resource. Significant efforts have been put into the study of entanglement degradation in the presence of a realistic noisy environment. Here, we present a theoretical and an experimental study of the decoherence properties of entangled pairs of qubits. The entanglement dynamics of maximally entangled qubit pairs is shown to be related in a simple way to the noise representation in the Bloch sphere picture. We derive the entanglement level in the case when both qubits of a Bell state are transmitted through any arbitrary unital Pauli channel, and compare it to the case when the channel is applied only to one of the qubits. The dynamics of both cases was verified experimentally using an all-optical setup. We further investigated the evolution of partially entangled initial states. Different dynamics was observed for initial mixed and pure states of the same entanglement level.
Quantum entanglement at ambient conditions in a macroscopic solid-state spin ensemble.
Klimov, Paul V; Falk, Abram L; Christle, David J; Dobrovitski, Viatcheslav V; Awschalom, David D
2015-11-01
Entanglement is a key resource for quantum computers, quantum-communication networks, and high-precision sensors. Macroscopic spin ensembles have been historically important in the development of quantum algorithms for these prospective technologies and remain strong candidates for implementing them today. This strength derives from their long-lived quantum coherence, strong signal, and ability to couple collectively to external degrees of freedom. Nonetheless, preparing ensembles of genuinely entangled spin states has required high magnetic fields and cryogenic temperatures or photochemical reactions. We demonstrate that entanglement can be realized in solid-state spin ensembles at ambient conditions. We use hybrid registers comprising of electron-nuclear spin pairs that are localized at color-center defects in a commercial SiC wafer. We optically initialize 10(3) identical registers in a 40-μm(3) volume (with [Formula: see text] fidelity) and deterministically prepare them into the maximally entangled Bell states (with 0.88 ± 0.07 fidelity). To verify entanglement, we develop a register-specific quantum-state tomography protocol. The entanglement of a macroscopic solid-state spin ensemble at ambient conditions represents an important step toward practical quantum technology.
Quantum communication for satellite-to-ground networks with partially entangled states
陈娜; 权东晓; 裴昌幸; 杨宏
2015-01-01
To realize practical wide-area quantum communication, a satellite-to-ground network with partially entangled states is developed in this paper. For efficiency and security reasons, the existing method of quantum communication in distributed wireless quantum networks with partially entangled states cannot be applied directly to the proposed quantum network. Based on this point, an efficient and secure quantum communication scheme with partially entangled states is presented. In our scheme, the source node performs teleportation only after an end-to-end entangled state has been established by entanglement swapping with partially entangled states. Thus, security of quantum communication is guaranteed. The destination node recovers the transmitted quantum bit with the help of auxiliary quantum bit and specially defined unitary matrices. Detailed calculations and simulation analyses show that in the presented scheme, the probability of successfully transferring a quantum bit is high. In addition, the auxiliary quantum bit provides a heralded mechanism for successful communication. Based on these critical components presented in this article, an efficient, secure, and practical wide-area quantum communication can be achieved.
Tight bound on coherent-state-based entanglement generation over lossy channels
Azuma, Koji; Koashi, Masato; Imoto, Nobuyuki
2009-01-01
The first stage of the hybrid quantum repeaters is entanglement generation based on transmission of pulses in coherent states over a lossy channel. Protocols to make entanglement with only one type of error are favorable for rendering subsequent entanglement distillation efficient. Here we provide the tight upper bound on performances of these protocols that is determined only by the channel loss. In addition, we show that this bound is achievable by utilizing a proposed protocol [arXiv:0811.3100] composed of a simple combination of linear optical elements and photon-number-resolving detectors.
Entanglement concentration for multi-atom GHZ class state via cavity QED
Jiang Chun-Lei; Fang Mao-Fa; Zheng Xiao-Juan
2006-01-01
In this paper, we propose a physical scheme to concentrate non-maximally entangled atomic pure states by using atomic collision in a far-off-resonant cavity. The most distinctive advantage of our scheme is that the non-maximally entangled atoms 05 be far from or near each other and their degree of entanglement can be maximally amplified. The photon-number-dependent parts in the effective Hamiltonian are cancelled with the assistance of a strong classical field,thus the scheme is insensitive to both the cavity decay and the thermal field.
Multi-mode Einstein-Podolsky-Rosen Entangled State Representation and Its Applications
LI Heng-Mei; YUAN Hong-Chun
2008-01-01
Our primary purpose of this work is to explicitly construct the general multipartite Einstein Podolsky-Rosen (EPR) entangled state in multi-mode Foek space for a system with different masses of particles,which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property.Its entanglement can be seen more clearly by analyzing its standard Sehmidt decomposition.In addition,some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.
Entanglement Dynamics of Two-Qubit System in Different Types of Noisy Channels
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.
Efficient entanglement purification in quantum repeaters
Sheng Yu-Bo; Zhou Lan; Cheng Wei-Wen; Gong Long-Yan; Zhao Sheng-Mei; Zheng Bao-Yu
2012-01-01
We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics.With the CNOT gates,our EPP can reach a higher fidelity than the conventional one.Moreover,it does not require the fidelity of the initial mixed state to satisfy · · 1· 2.If the initial state is not entangled,it still can be purified.With the linear optics,this protocol can get pure maximally entangled pairs with some probabilities.Meanwhile,it can be used to purify the entanglement between the atomic ensembles in distant locations.This protocol may be useful in long-distance quantum communication.
[Treatment of depressive mixed states].
Dubois, M; Dassa, D; Belzeaux, R; Fakra, E; Cermolacce, M; Corréard, N; Kaladjian, A; Azorin, J-M
2013-12-01
Mixed states are a frequent mood state characterized by the mixture of manic and depressive symptoms. Their clinical description has been studied for centuries but has known a renewal of interest recently. Several authors intend to redefine its diagnostic criteria to develop an appropriate therapeutic strategy. Current recommendations suggest to treat mixed depression as a mixed state whatever the dominant polarity is, and therefore according to the rules of therapeutic management of the manic state. Mood stabilizers and antipsychotic medications are indicated and have proven their effectiveness. Lithium, which was considered controversial, now appears to have some therapeutic value, especially in the prevention of suicidal behavior. The depressive component of mixed states, even pronounced, should not be an argument for a prescription of antidepressants, at the risk of aggravating clinical components such as irritability and impulsivity and increasing the danger of suicide attempt. Furthermore, electroconvulsivetherapy represents a real alternative ; psychotherapies have their place in relapse prevention and psychoeducation, but not during acute phases. Finally, an accurate assessment and appropriate management of suicide risk should be a constant concern for the clinicians. Copyright © 2013 L’Encéphale. Published by Elsevier Masson SAS.. All rights reserved.
Is composite noise necessary for sudden death of entanglement?
Yashodamma, K. O.; Sudha
The finite time disentanglement or entanglement sudden death, when only one part of the composite system is subjected to a single noise, is examined. While it is shown that entanglement sudden death can occur when a part of the entangled mixed state is subjected to either amplitude noise or phase noise, local action of either of them does not cause entanglement sudden death in pure entangled states. In contrast, depolarizing noise is shown to have an ability to cause sudden death of entanglement even in pure entangled states, when only one part of the state is exposed to it. The result is illustrated through the action of different noisy environments individually on a single qubit of the so-called X class of states and an arbitrary two-qubit pure state.
Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States
Z. Y. Xie
2014-02-01
Full Text Available We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS, for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.
Exact stabilization of entangled states in finite time by dissipative quantum circuits
Johnson, Peter D.; Ticozzi, Francesco; Viola, Lorenza
2017-07-01
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly noncanonical) commuting parent Hamiltonian may be found. Aside from graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi [Quantum Inf. Comput. 5, 187 (2005)]. Extensions to representative classes of mixed graph-product and thermal states are also discussed.
Laurat, Julien [Laboratoire Kastler Brossel, Case 74, Universite Pierre et Marie curie, 4 Place Jussieu, 75252 Paris cedex 05 (France); Keller, Gaelle [Laboratoire Kastler Brossel, Case 74, Universite Pierre et Marie curie, 4 Place Jussieu, 75252 Paris cedex 05 (France); Oliveira-Huguenin, Jose Augusto [Laboratoire Kastler Brossel, Case 74, Universite Pierre et Marie curie, 4 Place Jussieu, 75252 Paris cedex 05 (France); Fabre, Claude [Laboratoire Kastler Brossel, Case 74, Universite Pierre et Marie curie, 4 Place Jussieu, 75252 Paris cedex 05 (France); Coudreau, Thomas [Laboratoire Kastler Brossel, Case 74, Universite Pierre et Marie curie, 4 Place Jussieu, 75252 Paris cedex 05 (France); Laboratoire Materiaux et Phenomenes Quantiques, Case 7021, Universite Denis Diderot, 2 Place Jussieu, 75251 Paris cedex 05 (France); Serafini, Alessio [Dipartimento di Fisica ' E R Caianiello' , Universita di Salerno (Italy); CNR-Coherentia, Gruppo di Salerno (Italy); and INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S Allende, 84081 Baronissi (Saudi Arabia) (Italy); Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Adesso, Gerardo [Dipartimento di Fisica ' E R Caianiello' , Universita di Salerno (Italy); CNR-Coherentia, Gruppo di Salerno (Italy); and INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S Allende, 84081 Baronissi (Saudi Arabia) (Italy); Illuminati, Fabrizio [Dipartimento di Fisica ' E R Caianiello' , Universita di Salerno (Italy) and CNR-Coherentia, Gruppo di Salerno (Italy) and INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S Allende, 84081 Baronissi (SA) (Italy)
2005-12-01
A powerful theoretical structure has emerged in recent years on the characterization and quantification of entanglement in continuous-variable systems. After reviewing this framework, we will illustrate it with an original set-up based on a type-II OPO (optical parametric oscillator) with adjustable mode coupling. Experimental results allow a direct verification of many theoretical predictions and provide a sharp insight into the general properties of two-mode Gaussian states and entanglement resource manipulation.
无
2006-01-01
We propose a scheme for generating a maximally entangled state of two three-level superconducting quantum interference devices (SQUIDs) by using a quantized cavity field and classical microwave pluses in cavity. In this scheme, no quantum information will be transferred from the SQUIDs to the cavity since the cavity field is only virtually excited. Thus, the cavity decay is suppressed during the entanglement generation.
Laurat, J; Oliveira-Huguenin, J A; Fabre, C; Coudreau, T; Serafini, A; Adesso, G; Illuminati, F; Laurat, Julien; Keller, Ga\\"{e}lle; Oliveira-Huguenin, Jose-Augusto; Fabre, Claude; Coudreau, Thomas; Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
A powerful theoretical structure has emerged in recent years on the characterization and quantification of entanglement in continuous-variable systems. After reviewing this framework, we will illustrate it with an original set-up based on a type-II OPO with adjustable mode coupling. Experimental results allow a direct verification of many theoretical predictions and provide a sharp insight into the general properties of two-mode Gaussian states and entanglement resource manipulation.
Entanglement and purity of two-mode Gaussian states in noisy channels
Serafini, A; Paris, M G A; De Siena, S; Serafini, Alessio; Illuminati, Fabrizio; Paris, Matteo G. A.; Siena, Silvio De
2004-01-01
We study the evolution of purity, entanglement and total correlations of general two--mode Gaussian states of continuous variable systems in arbitrary uncorrelated Gaussian environments. The time evolution of purity, Von Neumann entropy, logarithmic negativity and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.
Wu, Jin-Lei; Ji, Xin; Zhang, Shou
2017-01-01
We propose a dressed-state scheme to achieve shortcuts to adiabaticity in atom-cavity quantum electrodynamics for speeding up adiabatic two-atom quantum state transfer and maximum entanglement generation. Compared with stimulated Raman adiabatic passage, the dressed-state scheme greatly shortens the operation time in a non-adiabatic way. By means of some numerical simulations, we determine the parameters which can guarantee the feasibility and efficiency both in theory and experiment. Besides, numerical simulations also show the scheme is robust against the variations in the parameters, atomic spontaneous emissions and the photon leakages from the cavity.
A scheme for transferring an unknown atomic entangled state via cavity quantum electrodynamics
Wu Tao; Ye Liu; Ni Zhi-Xiang
2006-01-01
In this paper, we propose a scheme for transferring an unknown atomic entangled state via cavity quantum electrodynamics (QED). This scheme, which has a successful probability of 100 percent, does not require Bell-state measurement and performing any operations to reconstruct an initial state. Meanwhile, the scheme only involves atomfield interaction with a large detuning and does not require the transfer of quantum information between the atoms and cavity. Thus the scheme is insensitive to the cavity field states and cavity decay. This scheme can also be extended to transfer ring an entangled state of n-atom.
Tomographic reconstruction of time-bin-entangled qudits
Nowierski, Samantha J.; Oza, Neal N.; Kumar, Prem; Kanter, Gregory S.
2016-10-01
We describe an experimental implementation to generate and measure high-dimensional time-bin-entangled qudits. Two-photon time-bin entanglement is generated via spontaneous four-wave mixing in single-mode fiber. Unbalanced Mach-Zehnder interferometers transform selected time bins to polarization entanglement, allowing standard polarization-projective measurements to be used for complete quantum state tomographic reconstruction. Here we generate maximally entangled qubits (d =2 ) , qutrits (d =3 ) , and ququarts (d =4 ) , as well as other phase-modulated nonmaximally entangled qubits and qutrits. We reconstruct and verify all generated states using maximum-likelihood estimation tomography.
Multipartite entanglement indicators based on monogamy relations of n-qubit symmetric states.
Liu, Feng; Gao, Fei; Qin, Su-Juan; Xie, Shu-Cui; Wen, Qiao-Yan
2016-02-04
Constructed from Bai-Xu-Wang-class monogamy relations, multipartite entanglement indicators can detect the entanglement not stored in pairs of the focus particle and the other subset of particles. We investigate the k-partite entanglement indicators related to the αth power of entanglement of formation (αEoF) for k ≤ n, αϵ and n-qubit symmetric states. We then show that (1) The indicator based on αEoF is a monotonically increasing function of k. (2) When n is large enough, the indicator based on αEoF is a monotonically decreasing function of α, and then the n-partite indicator based on works best. However, the indicator based on 2 EoF works better when n is small enough.
Generation of the quadripartite Greenberger-Horne-Zeilinger entangled state in quantum beat lasers
Wang, Fei
2013-12-01
In this letter, a scheme is presented to obtain quadripartite Greenberger-Horne-Zeilinger (GHZ) entanglement via quantum beats in a four-level diamond configuration atomic system. When the top and the ground states are initially prepared in a coherent superposition, the four quantized fields coupling with four dipole-allowed transitions can be correlated with each other by using a strong microwave field to drive the dipole-forbidden transition. It is the combined effect of atomic coherence-controlled correlated-spontaneous emission and double quantum beats that results in the quadripartite GHZ-type entanglement. Our numerical results show that the quadripartite entanglement, which can be controlled effectively by varying the amplitude and phase of the microwave field, occurs in a very wide parameter range. In addition, using input-output theory, we find that the output quadripartite entanglement is robust against thermal fluctuations, which may be useful for long-distance quantum communications.
Tomography of the quantum state of photons entangled in high dimensions
Agnew, Megan; Leach, Jonathan [Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5 Canada (Canada); McLaren, Melanie; Roux, F. Stef [CSIR National Laser Centre, Pretoria 0001 (South Africa); Boyd, Robert W. [Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5 Canada (Canada); Institute of Optics, University of Rochester, Rochester, New York 14627 (United States)
2011-12-15
Systems entangled in high dimensions have recently been proposed as important tools for various quantum information protocols, such as multibit quantum key distribution and loophole-free tests of nonlocality. It is therefore important to have precise knowledge of the nature of such entangled quantum states. We tomographically reconstruct the quantum state of the two photons produced by parametric downconversion that are entangled in a d-dimensional orbital angular momentum basis. We determine exactly the density matrix of the entangled two-qudit state with d ranging from 2 to 8. The recording of higher-dimensional states is limited only by the number of data points required and therefore the length of time needed to complete the measurements. We find all the measured states to have fidelities and linear entropies that satisfy the criteria required for a violation of the appropriate high-dimensional Bell inequality. Our results therefore precisely characterize the nature of the entanglement, thus establishing the suitability of such states for applications in quantum information science.
Proposal for demonstration of long-range cluster state entanglement in the presence of photon loss
Thomas Nutz
2017-06-01
Full Text Available Photonic cluster states are a crucial resource for optical quantum computing. Recently a quantum dot single photon source has been demonstrated to produce strings of single photons in a small linear cluster state. Sources of this kind could produce much larger cluster states, but high photon loss rates make it impossible to characterize the entanglement generated by quantum state tomography. We present a benchmarking method for such sources that can be used to demonstrate useful long-range entanglement with currently available collection/detection efficiencies below 1%. The measurement of the polarization state of single photons in different bases can provide an estimate for the three-qubit correlation function ⟨ZXZ⟩. This value constrains correlations spanning more than three qubits, which in turn provide a lower bound for the localizable entanglement between any two qubits in the large state produced by the source. Finite localizable entanglement can be established by demonstrating ⟨ZXZ⟩>23. This result enables photonic experiments demonstrating computationally useful entanglement with currently available technology.