A nonextensive critical phenomenon scenario for quantum entanglement

Abstract

We discuss the paradigmatic bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen fully entangled state $|{\Psi }^{-}$$>\equiv \frac{1}{\sqrt{2}}(|$$\uparrow {>}_A|$$\downarrow {>}_B$$-|$$\downarrow {>}_A|$$\uparrow {>}_B)$ and $\frac{3(1-x)}{4}$ of being orthogonal. This system is known to be separable if and only if $x\le 1/3$ (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form $S_q\equiv \frac{1-Tr{\rho }^q}{q-1}(q\in \mathcal{R};$$S_1$$=-$ $Tr$ $\rho \ln \rho )$ 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.

To appear in Physica A, Proceedings of the IUPAP Workshop on New Trends on Fractal Aspects of Complex Systems (16 - 20 October 2000, Maceio-AL, Brazil), ed. M.L. Lyra (Elsevier, Amsterdam, 2001); 8 PS figures

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Cited by in corpus (9)

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• Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics
• Maximally Entangled Mixed States and Conditional Entropies
• Some Features of the Conditional $q$-Entropies of Composite Quantum Systems
• Frontier between separability and quantum entanglement in a many spin system
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Inclusion relations among separability criteria
• On the Correlations Between Quantum Entanglement and q-Information Measures