A nonextensive critical phenomenon scenario for quantum entanglement

We discuss the paradigmatic bipartite spin-1/2 system having the probabilit ies (1 + 3x)/4 of being in the Einstein-Podolsky-Rosen fully entangled stat e \ Psi (-)> equivalent to 1/root2(\ up arrow > (A)\ down arrow > (B)-\ dow n arrow > (A)\ up arrow > (B)) and 3(1 - x)/4 of being orthogonal. This sys tem is known to be separable if and only if x less than or equal to 1/3 (Pe res criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form S-q equivalent to (1 - Tr rho (q))/(q - 1) (q epsilon R; S-1 = -Tr rho ln rho) which has e nabled a current generalization of Boltzmann-Gibbs statistical mechanics. T his result has been enrichened by Lloyd, Baranger and one of the present au thors by proposing a critical-phenomenon-like scenario for quantum entangle ment. Here, we further illustrate and discuss this scenario through the cal culation of some relevant quantities. (C) 2001 Elsevier Science B.V. All ri ghts reserved.