This is an announcement for the paper "The volume of separable states is super-doubly-exponentially small" by Stanislaw Szarek.

Abstract: In this note we give sharp estimates on the volume of the set of separable states on N qubits. In particular, the magnitude of the "effective radius" of that set in the sense of volume is determined up to a factor which is a (small) power of N, and thus precisely on the scale of powers of its dimension. Additionally, one of the appendices contains sharp estimates (by known methods) for the expected values of norms of the GUE random matrices. We employ standard tools of classical convexity, high-dimensional probability and geometry of Banach spaces.

Archive classification: Quantum Physics; Functional Analysis

Remarks: 20 p., LATEX; an expanded version of the original submission: more background material from convexity and geometry of Banach spaces, more exhaustive bibliography and improved quality of references to the bibliography

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/quant-ph/0310061

or

http://arXiv.org/abs/quant-ph/0310061

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uget /0310061

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get /0310061

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