Robustness of entanglement

Vidal, Guifré; Tarrach, R.

doi:10.1103/physreva.59.141

Cited by 571 publications

(733 citation statements)

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“…(18). One immediate criterion is that the state vectors lie in the Hilbert subspace are all entangled as long as the corresponding nonzero components of the concurrence vectors for those bases have the same signs (i.e., positive or negative), which implies impossible to make a superposition state with all the components of the concurrence vector vanish.…”

Section: Concurrence Surface and Entanglement Edgementioning

confidence: 99%

“…Braunstein et al [17] analyzed the separability of N -qubit states near the maximally mixed state. Vidal and Tarrach [18] give a separability boundary for the mixture of the maximally mixed state with a pure state. Caves and Milburn [19] discussed the lower and upper bounds on the size of the neighborhood of separable states around the maximally mixed state of qutrits.…”

Section: Concurrence Surface and Entanglement Edgementioning

confidence: 99%

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Concurrence vectors for entanglement of high-dimensional systems

Zhu

2008

Front. Phys. China

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The concurrence vectors are proposed by employing the fundamental representation of An Lie algebra, which provides a clear criterion to evaluate the entanglement of bipartite system of arbitrary dimension for both pure and mixed states. Accordingly, a state is separable if the norm of its concurrence vector vanishes. The state vectors related to SU(3) states and SO(3) states are discussed in detail. The sign situation of nonzero components of concurrence vectors of entangled bases presents a simple criterion to judge whether the whole Hilbert subspace spanned by those bases is entangled, or there exists entanglement edge. This is illustrated in terms of the concurrence surfaces of several concrete examples.

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Section: Concurrence Surface and Entanglement Edgementioning

confidence: 99%

Section: Concurrence Surface and Entanglement Edgementioning

confidence: 99%

Concurrence vectors for entanglement of high-dimensional systems

Zhu

2008

Front. Phys. China

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“…So is another measure of entanglement called robustness, which is defined as the minimal amount of separable noise that has to be mixed with the analyzed state to wash out completely its quantum correlations [56,8]. For pure states the robustness equals N F max − 1 = exp(H 1/2 ) − 1.…”

Section: Local Transformations Of Pure Statesmentioning

confidence: 99%

Relativity of Pure States Entanglement

Życzkowski

Bengtsson

2002

Annals of Physics

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Entanglement of any pure state of an N × 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. C 2002 Elsevier Science (USA)

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“…An example of a quantifier that can be calculated using OEW is the Generalized Robustness of entanglement [22] ( R g (ρ)), which is defined as the minimum required mixture such that a separable state is obtained. Precisely, it is the minimum value of s such that…”

Section: A Witnessed Entanglementmentioning

confidence: 99%

Quantifying quantum correlations in fermionic systems using witness operators

Iemini

Maciel

Debarba

et al. 2012

Quantum Inf Process

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We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entanglement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robustness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann concurrence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.

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Robustness of entanglement

Cited by 571 publications

References 20 publications

Concurrence vectors for entanglement of high-dimensional systems

Concurrence vectors for entanglement of high-dimensional systems

Relativity of Pure States Entanglement

Quantifying quantum correlations in fermionic systems using witness operators

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