A nonextensive critical phenomenon scenario for quantum entanglement

Constantino Tsallis, Pedro W. Lamberti and Domingo Prato

Physica A: Statistical Mechanics and its Applications, 2001, vol. 295, issue 1, 158-171

Abstract: We discuss the paradigmatic bipartite spin-12 system having the probabilities (1+3x)/4 of being in the Einstein–Podolsky–Rosen fully entangled state |Ψ−〉≡1/2(|↑〉A|↓〉B−|↓〉A|↑〉B) and 3(1−x)/4 of being orthogonal. This system is known to be separable if and only if x⩽13 (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form Sq≡(1−Trρq)/(q−1)(q∈R;S1=−Trρlnρ) which has enabled a current generalization of Boltzmann–Gibbs statistical mechanics. This result has been enrichened by Lloyd, Baranger and one of the present authors by proposing a critical-phenomenon-like scenario for quantum entanglement. Here, we further illustrate and discuss this scenario through the calculation of some relevant quantities.

Keywords: Nonextensive statistical mechanics; Quantum entanglement; Separability (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:295:y:2001:i:1:p:158-171

DOI: 10.1016/S0378-4371(01)00070-X

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