Bell inequalities versus entanglement and mixedness for a class of two-qubit states

Derkacz, Łukasz; Jakóbczyk, Lech

doi:10.1016/j.physleta.2004.06.007

Cited by 11 publications

(16 citation statements)

References 19 publications

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“…Hence the image of the union Λ 1 ∪ Λ 2 is defined by (11) , which proves the theorem. It follows at once: Corollary 2 A sufficient condition for the fulfilment of all CHSH inequalities is that the linear entropy of the state fulfils S 12 ≥ 1 2…”

Section: Bell Inequalities and Linear Entropysupporting

confidence: 58%

Entropy inequalities and Bell inequalities for two-qubit systems

Santos

2004

Phys. Rev. A

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Section: Bell Inequalities and Linear Entropysupporting

confidence: 58%

Entropy inequalities and Bell inequalities for two-qubit systems

Santos

2004

Phys. Rev. A

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“…Note that many other comparative studies of the concurrence and CHSH violation were limited to some specific classes of two-qubit states usually in a dynamical context [18][19][20][21][22][23][24][25][26].…”

Section: Arxiv:13066504v2 [Quant-ph] 19 Nov 2013mentioning

confidence: 99%

Entanglement estimation from Bell inequality violation

et al. 2013

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It is well known that the violation of Bell's inequality in the form given by Clauser, Horne, Shimony, and Holt (CHSH) in two-qubit systems requires entanglement, but not vice versa, i.e., there are entangled states which do not violate the CHSH inequality. Here we compare some standard entanglement measures with violations of the CHSH inequality (as given by the Horodecki measure) for two-qubit states generated by Monte Carlo simulations. We describe states that have extremal entanglement according to the negativity, concurrence, and relative entropy of entanglement for a given value of the CHSH violation. We explicitly find these extremal states by applying the generalized method of Lagrange multipliers based on the Karush-Kuhn-Tucker conditions. The found minimal and maximal states define the range of entanglement accessible for any two-qubit states that violate the CHSH inequality by the same amount. We also find extremal states for the concurrence versus negativity by considering only such states which do not violate the CHSH inequality. Furthermore, we describe an experimentally efficient linear-optical method to determine the highest Horodecki degree of the CHSH violation for arbitrary mixed states of two polarization qubits. By assuming to have access simultaneously to two copies of the states, our method requires only six discrete measurement settings instead of nine settings, which are usually considered.

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“…The reason as to why equal amount of Bell-CHSH violation requires different amounts of entanglement cannot be explained by mixedness alone [47]. For a class of bipartite qubit mixed states it has been shown that it is not possible to discriminate between states violating or not violating Bell-CHSH inequalities, knowing only their entanglement and mixedness [48].…”

Section: Qm Violation Of Gwi By Mixed Bipartite Qutrit Statesmentioning

confidence: 99%

Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

et al. 2017

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Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-MassarPopescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yielding the measurable marginal probabilities. Such generalized Wigner inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any two outcomes, and are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states using trichotomic observables defined by six-port beam splitter as well as by the spin-1 component observables. The efficacy of GWI is then probed in these cases by comparing the QM violation of GWI with that obtained for the CGLMP inequality. This comparison is done by incorporating white noise in the singlet and isotropic qutrit states. It is found that for the six-port beam splitter observables, QM violation of GWI is more robust than that of the CGLMP inequality for singlet qutrit states, while for isotropic qutrit states, QM violation of the CGLMP inequality is more robust. On the other hand, for the spin-1 component observables, QM violation of GWI is more robust for both the type of states considered.

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Bell inequalities versus entanglement and mixedness for a class of two-qubit states

Cited by 11 publications

References 19 publications

Entropy inequalities and Bell inequalities for two-qubit systems

Entropy inequalities and Bell inequalities for two-qubit systems

Entanglement estimation from Bell inequality violation

Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

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