Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane

Derkacz, Łukasz; Jakóbczyk, Lech

doi:10.1103/physreva.72.042321

Cited by 26 publications

(38 citation statements)

References 15 publications

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“…We study the relation between the CHSH violation and negativity (and other entanglement measures) for arbitrary two-qubit states analogously to the comparisons of the CHSH violation with the concurrence [14,17] and REE [15]. 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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Section: Arxiv:13066504v2 [Quant-ph] 19 Nov 2013mentioning

confidence: 99%

Entanglement estimation from Bell inequality violation

et al. 2013

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“…Projection of this curve on twodimensional spaces clearly shows the absence of one-toone correspondence between couples of the quantifiers C, P and B [25]. This dynamical feature is maintained even in the limit of perfect cavity suffering no losses.…”

Section: Discussionmentioning

confidence: 88%

“…The analysis above shows that a quite complex interplay occurs among C, P and B. It is known that in general, given two of these quantities, this does not determine the third [25]. However, one may ask if it may happen that some explicit connections among them exist, which can be expressed in a closed form for some class of states.…”

Section: Perfect Cavitymentioning

confidence: 99%

“…When B is larger than the classical threshold 2, no classical local model may reproduce all correlations of these states. The three functions u j are [25] …”

Section: Dynamics In C-p -B Space For Common Reservoirmentioning

confidence: 99%

“…However, there are states having the same amount of entanglement and mixedness but different values of the Bell function [23]. Relations between entanglement, mixedness and Bell function have been given analytically for a restrict [24], and numerically for a more general [25] class of states. In particular, there are regions of the concurrence-linear entropy plane where, given concurrence and linear entropy, two families of states can be discriminated: all states from one family violate the Clauser-Horne-Shimony-Holt (CHSH) form of Bell inequality while all states from the other family satisfy it.…”

Section: Introductionmentioning

confidence: 99%

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Connection among entanglement, mixedness, and nonlocality in a dynamical context

et al. 2010

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We investigate the dynamical relations among entanglement, mixedness and nonlocality, quantified by concurrence C, purity P and maximum of Bell function B, respectively, in a system of two qubits in a common structured reservoir. To this aim we introduce the C-P -B parameter space and analyze the time evolution of the point representative of the system state in such a space. The dynamical interplay among entanglement, mixedness and nonlocality strongly depends on the initial state of the system. For a two-excitation Bell state the representative point draws a multi-branch curve in the C-P -B space and we show that a closed relation among these quantifiers does not hold. By extending the known relation between C and B for pure states, we give an expression among the three quantifiers for mixed states. In this equation we introduce a quantity, vanishing for pure states which has not in general a closed form in terms of C, P and B. Finally we demonstrate that for an initial one-excitation Bell state a closed C-P -B relation instead exists and the system evolves remaining always a maximally entangled mixed state.

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