dorsal/arxiv
View SchemaOptimal, reliable estimation of quantum states
| Authors | Robin Blume-Kohout |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611080 |
| URL | https://arxiv.org/abs/quant-ph/0611080 |
| DOI | 10.1088/1367-2630/12/4/043034 |
| Journal | New J. Phys. 12, 043034 (2010) |
Abstract
Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE), generally reports an estimate with zero eigenvalues. These cannot be justified. Furthermore, the MLE estimate is incompatible with error bars, so conclusions drawn from it are suspect. I propose an alternative procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues, its eigenvalues provide a bound on their own uncertainties, and it is the most accurate procedure possible. I show how to implement BME numerically, and how to obtain natural error bars that are compatible with the estimate. Finally, I briefly discuss the differences between Bayesian and frequentist estimation techniques.
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"abstract": "Accurately inferring the state of a quantum device from the results of\nmeasurements is a crucial task in building quantum information processing\nhardware. The predominant state estimation procedure, maximum likelihood\nestimation (MLE), generally reports an estimate with zero eigenvalues. These\ncannot be justified. Furthermore, the MLE estimate is incompatible with error\nbars, so conclusions drawn from it are suspect. I propose an alternative\nprocedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues,\nits eigenvalues provide a bound on their own uncertainties, and it is the most\naccurate procedure possible. I show how to implement BME numerically, and how\nto obtain natural error bars that are compatible with the estimate. Finally, I\nbriefly discuss the differences between Bayesian and frequentist estimation\ntechniques.",
"arxiv_id": "quant-ph/0611080",
"authors": [
"Robin Blume-Kohout"
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"doi": "10.1088/1367-2630/12/4/043034",
"journal_ref": "New J. Phys. 12, 043034 (2010)",
"title": "Optimal, reliable estimation of quantum states",
"url": "https://arxiv.org/abs/quant-ph/0611080"
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