dorsal/arxiv
View SchemaThe volume of separable states is super-doubly-exponentially small
| Authors | Stanislaw Szarek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310061 |
| URL | https://arxiv.org/abs/quant-ph/0310061 |
| DOI | 10.1103/PhysRevA.72.032304 |
| Journal | Phys. Rev. A 72, 032304 (2005) |
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.
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"abstract": "In this note we give sharp estimates on the volume of the set of separable\nstates on N qubits. In particular, the magnitude of the \"effective radius\" of\nthat set in the sense of volume is determined up to a factor which is a (small)\npower of N, and thus precisely on the scale of powers of its dimension.\nAdditionally, one of the appendices contains sharp estimates (by known methods)\nfor the expected values of norms of the GUE random matrices. We employ standard\ntools of classical convexity, high-dimensional probability and geometry of\nBanach spaces.",
"arxiv_id": "quant-ph/0310061",
"authors": [
"Stanislaw Szarek"
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"doi": "10.1103/PhysRevA.72.032304",
"journal_ref": "Phys. Rev. A 72, 032304 (2005)",
"title": "The volume of separable states is super-doubly-exponentially small",
"url": "https://arxiv.org/abs/quant-ph/0310061"
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