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When is a Statistical Operator Separable?

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When is a Statistical Operator Separable?

– A Comparison of Different Definitions

Thomas Kr¨uger

Institute of Chemistry, Karl-Franzens-University Graz, Strassoldogasse 10, A-8010 Graz, Austria Reprint requests to Dr. T. K.; Fax: +43 316 380 9893, E-mail: thomas.krueger@kfunigraz.ac.at Z. Naturforsch. 56 a, 849–854 (2001); received September 2, 2001

Quantum correlations are based on the non-separability of the total system’s statistical operator.

The notion of non-separability, on the other hand, is given with respect to the precise meaning of separability only. So it is a crucial task to define separability in terms of statistical operators.

A recently proposed approach offers several advantages with respect to the usual definition. The von Neumann entropySallows to develop a measureIa=bof the relative non-separability of an operatorawith respect to another operatorb. This is a system immanent quantity of any property type as, e. g. spin or polarization. We compare the effect of the different approaches onSandIa=b. Finally, the applicability of a common separability criterion will be checked.

Key words: Statistical Operators; von Neumann Entropy; Separability.

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