A nonextensive critical phenomenon scenario for quantum entanglement

We discuss the paradigmatic bipartite spin- system having the probabilities (1+3x)/4 of being in the Einstein–Podolsky–Rosen fully entangled state and 3(1−x)/4 of being orthogonal. This system is known to be separable if and only if (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form S1=−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.