Note on separability of the Werner states in arbitrary dimensions

Pittenger, A. O.; Rubin, Morton H.

doi:10.1016/s0030-4018(00)00612-x

Cited by 53 publications

(79 citation statements)

References 8 publications

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“…We note that such mixed states are known to be maximally entangled [38,39]. [28,40]. The critical value for violation of a complete set of standard Bell inequalities for correlation functions equals Υ lr = 1/ √ 2 N −1 (see [31]).…”

Section: Colored Noisementioning

confidence: 99%

Entanglement and communication-reducing properties of noisyN-qubit states

et al. 2010

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We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -not requiring their further modification via stochastic local operations and classical communication such as entanglement purification or distillation procedures. We identify novel families of multi-particle states which are entangled but nevertheless allow local realistic description of specific Bell experiments. For some of them, the "gap" between the critical values for entanglement and violation of Bell inequality remains finite even in the limit of infinitely many qubits.

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Section: Colored Noisementioning

confidence: 99%

Entanglement and communication-reducing properties of noisyN-qubit states

et al. 2010

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“…This initial quantum state σ c is non-separable if and only if λ > λ D = (1 + D) −1 [19] so that a purification scheme can succeed only for those values of λ.…”

Section: Bipartite Purification In Higher Dimensional Spacesmentioning

confidence: 99%

Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces

Alber

Delgado

Gisin

et al. 2001

J. Phys. A: Math. Gen.

122

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A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of nonlinear quantum maps is generated in a natural way by a hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other know purification schemes.

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“…As a result, studies of the separability for SGWS itself is of great importance. In [24,25,26], Arthur O. Pittenger and Morton H. Rubin presented a necessary and sufficient condition of separability for a special case, they proved that, for |ψ In this letter, we shall provide a necessary and sufficient condition of separability for the SGWS. Our main result is as follows:…”

mentioning

confidence: 94%

Sufficient and necessary condition of separability for generalized Werner states

Deng

Chen

2009

Annals of Physics

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We introduce a sufficient and necessary condition for the separability of a specific class of N ddimensional system (qudits) states, namely special generalized Werner state (SGWS):is an entangled pure state of N qudits system and αi satisfys two restrictions: (i), where T = Min i =j {1/|αiαj|}, is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.

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Note on separability of the Werner states in arbitrary dimensions

Cited by 53 publications

References 8 publications

Entanglement and communication-reducing properties of noisyN-qubit states

Entanglement and communication-reducing properties of noisyN-qubit states

Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces

Sufficient and necessary condition of separability for generalized Werner states

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