dorsal/arxiv
View SchemaQuantum State Reconstruction From Incomplete Data
| Authors | V. Buzek, G. Drobny, R. Derka, G. Adam, H. Wiedemann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9805020 |
| URL | https://arxiv.org/abs/quant-ph/9805020 |
Abstract
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined only when measurements on infinite ensembles of identically prepared quantum systems are performed. But how one can estimate (guess) quantum state when just incomplete data are available (known)? What is the most reliable estimation based on a given measured data? What is the optimal measurement providing only a finite number of identically prepared quantum objects are available? These are some of the questions we address. We present several schemes for a reconstruction of states of quantum systems from measured data: (1) We show how the maximum entropy (MaxEnt) principle can be efficiently used for an estimation of quantum states on incomplete observation levels. (2) We show how Bayesian inference can be used for reconstruction of quantum states when only a finite number of identically prepared systems are measured. (3) We describe the optimal generalized measurement of a finite number of identically prepared quantum systems which results in the estimation of a quantum state with the highest fidelity.
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"abstract": "Knowing and guessing, these are two essential epistemological pillars in the\ntheory of quantum-mechanical measurement. As formulated quantum mechanics is a\nstatistical theory. In general, a priori unknown states can be completely\ndetermined only when measurements on infinite ensembles of identically prepared\nquantum systems are performed. But how one can estimate (guess) quantum state\nwhen just incomplete data are available (known)? What is the most reliable\nestimation based on a given measured data? What is the optimal measurement\nproviding only a finite number of identically prepared quantum objects are\navailable? These are some of the questions we address. We present several\nschemes for a reconstruction of states of quantum systems from measured data:\n(1) We show how the maximum entropy (MaxEnt) principle can be efficiently used\nfor an estimation of quantum states on incomplete observation levels. (2) We\nshow how Bayesian inference can be used for reconstruction of quantum states\nwhen only a finite number of identically prepared systems are measured. (3) We\ndescribe the optimal generalized measurement of a finite number of identically\nprepared quantum systems which results in the estimation of a quantum state\nwith the highest fidelity.",
"arxiv_id": "quant-ph/9805020",
"authors": [
"V. Buzek",
"G. Drobny",
"R. Derka",
"G. Adam",
"H. Wiedemann"
],
"categories": [
"quant-ph"
],
"title": "Quantum State Reconstruction From Incomplete Data",
"url": "https://arxiv.org/abs/quant-ph/9805020"
},
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