A nonextensive critical phenomenon scenario for quantum entanglement

Abstract

We discuss the paradigmatic bipartite spin- 1 2 system having the probabilities (1+3 x)/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⩽ 1 3 (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form S q≡(1−Tr ρ q)/(q−1) (q∈ R; S 1=−Tr ρ ln ρ) 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.