[Banach] Abstract of a paper by Stanislaw Szarek
alspach at www.math.okstate.edu
Wed Jul 14 10:11:39 CDT 2004
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
The paper may be downloaded from the archive by web browser from URL
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to: math at arXiv.org.
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