dorsal/arxiv
View SchemaOptimal estimation of a physical observable's expectation value for pure states
| Authors | A. Hayashi, M. Horibe, T. Hashimoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512037 |
| URL | https://arxiv.org/abs/quant-ph/0512037 |
| DOI | 10.1103/PhysRevA.73.062322 |
| Journal | Phys. Rev. A 73, 062322 (2006) |
Abstract
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged over all pure states distributed in a unitary invariant way. We find that the optimal estimation is "biased", though the optimal measurement is given by successive projective measurements of the observable. The optimal estimate is not the sample average of observed data, but the arithmetic average of observed and "default nonobserved" data, with the latter consisting of all eigenvalues of the observable.
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"abstract": "We study the optimal way to estimate the quantum expectation value of a\nphysical observable when a finite number of copies of a quantum pure state are\npresented. The optimal estimation is determined by minimizing the squared error\naveraged over all pure states distributed in a unitary invariant way. We find\nthat the optimal estimation is \"biased\", though the optimal measurement is\ngiven by successive projective measurements of the observable. The optimal\nestimate is not the sample average of observed data, but the arithmetic average\nof observed and \"default nonobserved\" data, with the latter consisting of all\neigenvalues of the observable.",
"arxiv_id": "quant-ph/0512037",
"authors": [
"A. Hayashi",
"M. Horibe",
"T. Hashimoto"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.062322",
"journal_ref": "Phys. Rev. A 73, 062322 (2006)",
"title": "Optimal estimation of a physical observable\u0027s expectation value for pure states",
"url": "https://arxiv.org/abs/quant-ph/0512037"
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