dorsal/arxiv
View SchemaStrategies to measure a quantum state
| Authors | Franz Embacher, Heide Narnhofer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310180 |
| URL | https://arxiv.org/abs/quant-ph/0310180 |
| DOI | 10.1016/j.aop.2003.12.002 |
Abstract
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a ``typical'' probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of ``best strategy'' (i.e. the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all ``best'' strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.
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"abstract": "We consider the problem of determining the mixed quantum state of a large but\nfinite number of identically prepared quantum systems from data obtained in a\nsequence of ideal (von Neumann) measurements, each performed on an individual\ncopy of the system. In contrast to previous approaches, we do not average over\nthe possible unknown states but work out a ``typical\u0027\u0027 probability distribution\non the set of states, as implied by the experimental data. As a consequence,\nany measure of knowledge about the unknown state and thus any notion of ``best\nstrategy\u0027\u0027 (i.e. the choice of observables to be measured, and the number of\ntimes they are measured) depend on the unknown state. By learning from\npreviously obtained data, the experimentalist re-adjusts the observable to be\nmeasured in the next step, eventually approaching an optimal strategy. We\nconsider two measures of knowledge and exhibit all ``best\u0027\u0027 strategies for the\ncase of a two-dimensional Hilbert space. Finally, we discuss some features of\nthe problem in higher dimensions and in the infinite dimensional case.",
"arxiv_id": "quant-ph/0310180",
"authors": [
"Franz Embacher",
"Heide Narnhofer"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2003.12.002",
"title": "Strategies to measure a quantum state",
"url": "https://arxiv.org/abs/quant-ph/0310180"
},
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