A nonextensive critical phenomenon scenario for quantum entanglement

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.