A nonextensive critical phenomenon scenario for quantum entanglement
Constantino Tsallis, Pedro W. Lamberti, Domingo Prato
Abstract
We discuss the paradigmatic bipartite spin-1/2 system having the probabilities 1+3x4 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 x1/3 (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form Sq 1- Tr ρqq-1 (q ∈ R; S1= - Tr ρ 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.
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