The volume of separable states is super-doubly-exponentially small

Details The volume of separable states is super-doubly-exponentially small The volume of separable states is super-doubly-exponentially small

2003-10-09

arxiv.org/abs/quant-ph/0310061v2

Phys. Rev. A 72, 032304 (2005)

Physics

Quantum Physics

20 p., LATEX; an expanded version of the original submission: more background material from convexity and geometry of Banach s

Scientific paper

10.1103/PhysRevA.72.032304

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.

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