dorsal/arxiv
View SchemaEntropy and information gain in quantum continual measurements
| Authors | Alberto Barchielli |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012115 |
| URL | https://arxiv.org/abs/quant-ph/0012115 |
| Journal | Quantum Communication, Computing, and Measurement 3, P. Tombesi and O. Hirota (eds.) (Kluwer, New York, 2001) pp. 49-57 |
Abstract
The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument, positive operator valued measure, etc., by using quantum stochastic differential equations and by using classical stochastic differential equations (SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same times Ozawa made developments in the theory of instruments and introduced the related notions of a posteriori states and of information gain [1]. In this paper we introduce a simple class of SDE's relevant to the theory of continual measurements and we recall how they are related to instruments and a posteriori states and, so, to the general formulation of quantum mechanics. Then we introduce and use the notion of information gain and the other results of the paper [1] inside the theory of continual measurements. [1] M. Ozawa, On information gain by quantum measurements of continuous observables, J. Math. Phys. 27 (1986) 759-763.
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"abstract": "The theory of measurements continuous in time in quantum mechanics (quantum\ncontinual measurements) has been formulated by using the notions of instrument,\npositive operator valued measure, etc., by using quantum stochastic\ndifferential equations and by using classical stochastic differential equations\n(SDE\u0027s) for vectors in Hilbert spaces or for trace-class operators. In the same\ntimes Ozawa made developments in the theory of instruments and introduced the\nrelated notions of a posteriori states and of information gain [1].\n In this paper we introduce a simple class of SDE\u0027s relevant to the theory of\ncontinual measurements and we recall how they are related to instruments and a\nposteriori states and, so, to the general formulation of quantum mechanics.\nThen we introduce and use the notion of information gain and the other results\nof the paper [1] inside the theory of continual measurements.\n [1] M. Ozawa, On information gain by quantum measurements of continuous\nobservables, J. Math. Phys. 27 (1986) 759-763.",
"arxiv_id": "quant-ph/0012115",
"authors": [
"Alberto Barchielli"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Communication, Computing, and Measurement 3, P. Tombesi\n and O. Hirota (eds.) (Kluwer, New York, 2001) pp. 49-57",
"title": "Entropy and information gain in quantum continual measurements",
"url": "https://arxiv.org/abs/quant-ph/0012115"
},
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