dorsal/arxiv
View SchemaFrom quantum Bayesian inference to quantum tomography
| Authors | R. Derka, V. Buzek, G. Adam, P. L. Knight |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9701029 |
| URL | https://arxiv.org/abs/quant-ph/9701029 |
Abstract
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In this case the estimation corresponds to an averaging over a generalized microcanonical ensemble of pure states satisfying a set of constraints imposed by the measured mean values of the observables under consideration. We show that via the ``purification'' ansatz, statistical mixtures can also be consistently reconstructed via the quantum Bayesian inference scheme. In this case the estimation corresponds to averaging over the generalized canonical ensemble of states satisfying the given constraints, and the reconstructed density operator maximizes the von Neumann entropy (i.e., this density operator is equal to the generalized canonical density operator which follows from the Jaynes principle of maximum entropy). We study in detail the reconstruction of the spin-1/2 density operator and discuss the logical connection between the three reconstruction schemes, i.e., (1) quantum Bayesian inference, (2) reconstruction via the Jaynes principle of maximum entropy, and (3) discrete quantum tomography.
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"abstract": "We derive an expression for a density operator estimated via Bayesian quantum\ninference in the limit of an infinite number of measurements.\n This expression is derived under the assumption that the reconstructed system\nis in a pure state. In this case the estimation corresponds to an averaging\nover a generalized microcanonical ensemble of pure states satisfying a set of\nconstraints imposed by the measured mean values of the observables under\nconsideration. We show that via the ``purification\u0027\u0027 ansatz, statistical\nmixtures can also be consistently reconstructed via the quantum Bayesian\ninference scheme. In this case the estimation corresponds to averaging over the\ngeneralized canonical ensemble of states satisfying the given constraints, and\nthe reconstructed density operator maximizes the von Neumann entropy (i.e.,\nthis density operator is equal to the generalized canonical density operator\nwhich follows from the Jaynes principle of maximum entropy). We study in detail\nthe reconstruction of the spin-1/2 density operator and discuss the logical\nconnection between the three reconstruction schemes, i.e., (1) quantum Bayesian\ninference, (2) reconstruction via the Jaynes principle of maximum entropy, and\n(3) discrete quantum tomography.",
"arxiv_id": "quant-ph/9701029",
"authors": [
"R. Derka",
"V. Buzek",
"G. Adam",
"P. L. Knight"
],
"categories": [
"quant-ph"
],
"title": "From quantum Bayesian inference to quantum tomography",
"url": "https://arxiv.org/abs/quant-ph/9701029"
},
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"variant": "snapshot-2026-03-01",
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