dorsal/arxiv
View SchemaRandom quantum correlations and density operator distributions
| Authors | Michael J. W. Hall |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9802052 |
| URL | https://arxiv.org/abs/quant-ph/9802052 |
| DOI | 10.1016/S0375-9601(98)00190-X |
| Journal | Phys.Lett. A242 (1998) 123-129 |
Abstract
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique unitarily-invariant measure on the Hilbert sphere. However, the problem is open for the general case where states are described by density operators. Here two approaches to the problem are investigated. The first approach assumes that the system is randomly correlated with a second system, where the ensemble of composite systems is described by a random pure state. Results for qubits randomly correlated with other systems are presented, including average entanglement entropies. It is shown that maximum correlation is guaranteed in the limit as one system becomes infinite-dimensional. The second approach relies on choosing a metric on the space of density operators, and generating a corresponding ensemble from the induced volume element. Comparisons between the approaches are made for qubits, for which the second approach (based on the Bures metric) yields the most symmetric, and hence the least informative, ensemble of density operators.
{
"annotation_id": "8f39b221-4924-4fa4-a1aa-94e26abbde9d",
"date_created": "2026-03-02T18:02:41.302000Z",
"date_modified": "2026-03-02T18:02:41.302000Z",
"file_hash": "e4ef8f3d3cbdfe690e703ec0221a70ba131d1eace6843306d3316a875423f9a0",
"private": false,
"record": {
"abstract": "Consider the question: what statistical ensemble corresponds to minimal prior\nknowledge about a quantum system ? For the case where the system is in fact\nknown to be in a pure state there is an obvious answer, corresponding to the\nunique unitarily-invariant measure on the Hilbert sphere. However, the problem\nis open for the general case where states are described by density operators.\nHere two approaches to the problem are investigated.\n The first approach assumes that the system is randomly correlated with a\nsecond system, where the ensemble of composite systems is described by a random\npure state. Results for qubits randomly correlated with other systems are\npresented, including average entanglement entropies. It is shown that maximum\ncorrelation is guaranteed in the limit as one system becomes\ninfinite-dimensional.\n The second approach relies on choosing a metric on the space of density\noperators, and generating a corresponding ensemble from the induced volume\nelement. Comparisons between the approaches are made for qubits, for which the\nsecond approach (based on the Bures metric) yields the most symmetric, and\nhence the least informative, ensemble of density operators.",
"arxiv_id": "quant-ph/9802052",
"authors": [
"Michael J. W. Hall"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(98)00190-X",
"journal_ref": "Phys.Lett. A242 (1998) 123-129",
"title": "Random quantum correlations and density operator distributions",
"url": "https://arxiv.org/abs/quant-ph/9802052"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a181ba2f-925c-4ebd-901f-79cd50b10bf5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}