dorsal/arxiv
View SchemaOn the volume of the set of mixed entangled states
| Authors | Karol Zyczkowski, Pawel Horodecki, Anna Sanpera, Maciej Lewenstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9804024 |
| URL | https://arxiv.org/abs/quant-ph/9804024 |
| DOI | 10.1103/PhysRevA.58.883 |
| Journal | Phys.Rev. A58 (1998) 883 |
Abstract
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, while separability is connected with quantum mixtures. In particular, states of sufficiently low purity are necessarily separable.
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"abstract": "A natural measure in the space of density matrices describing N-dimensional\nquantum systems is proposed. We study the probability P that a quantum state\nchosen randomly with respect to the natural measure is not entangled (is\nseparable). We find analytical lower and upper bounds for this quantity.\nNumerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate\nthat P decreases exponentially with N. Analysis of a conditional measure of\nseparability under the condition of fixed purity shows a clear dualism between\npurity and separability: entanglement is typical for pure states, while\nseparability is connected with quantum mixtures. In particular, states of\nsufficiently low purity are necessarily separable.",
"arxiv_id": "quant-ph/9804024",
"authors": [
"Karol Zyczkowski",
"Pawel Horodecki",
"Anna Sanpera",
"Maciej Lewenstein"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.58.883",
"journal_ref": "Phys.Rev. A58 (1998) 883",
"title": "On the volume of the set of mixed entangled states",
"url": "https://arxiv.org/abs/quant-ph/9804024"
},
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