dorsal/arxiv
View SchemaDecomposing generalized measurements into continuous stochastic processes
| Authors | Martin Varbanov, Todd A. Brun |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701117 |
| URL | https://arxiv.org/abs/quant-ph/0701117 |
| DOI | 10.1103/PhysRevA.76.032104 |
| Journal | Phys. Rev. A 76, 032104 (2007) |
Abstract
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be seen as the limit of a consecutive sequence of weak measurements. They are naturally described in terms of stochastic processes, or time-dependent random variables. We show that any generalized measurement can be decomposed as a sequence of weak measurements with a mathematical limit as a continuous stochastic process. We give an explicit construction for any generalized measurement, and prove that the resulting continuous evolution, in the long-time limit, collapses the state of the quantum system to one of the final states generated by the generalized measurement, being decomposed, with the correct probabilities. A prominent feature of the construction is the presence of a feedback mechanism--the instantaneous choice weak measurement at a given time depends on the outcomes of earlier measurements. For a generalized measurement with $n$ outcomes, this information is captured by a real $n$-vector on an $n$-simplex, which obeys a simple classical stochastic evolution.
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"abstract": "One of the broadest concepts of measurement in quantum theory is the\ngeneralized measurement. Another paradigm of measurement--arising naturally in\nquantum optics, among other fields--is that of continuous-time measurements,\nwhich can be seen as the limit of a consecutive sequence of weak measurements.\nThey are naturally described in terms of stochastic processes, or\ntime-dependent random variables. We show that any generalized measurement can\nbe decomposed as a sequence of weak measurements with a mathematical limit as a\ncontinuous stochastic process. We give an explicit construction for any\ngeneralized measurement, and prove that the resulting continuous evolution, in\nthe long-time limit, collapses the state of the quantum system to one of the\nfinal states generated by the generalized measurement, being decomposed, with\nthe correct probabilities. A prominent feature of the construction is the\npresence of a feedback mechanism--the instantaneous choice weak measurement at\na given time depends on the outcomes of earlier measurements. For a generalized\nmeasurement with $n$ outcomes, this information is captured by a real\n$n$-vector on an $n$-simplex, which obeys a simple classical stochastic\nevolution.",
"arxiv_id": "quant-ph/0701117",
"authors": [
"Martin Varbanov",
"Todd A. Brun"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.76.032104",
"journal_ref": "Phys. Rev. A 76, 032104 (2007)",
"title": "Decomposing generalized measurements into continuous stochastic processes",
"url": "https://arxiv.org/abs/quant-ph/0701117"
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