dorsal/arxiv
View SchemaQuantum stochastic approach to the description of quantum measurements
| Authors | Elena R. Loubenets |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109094 |
| URL | https://arxiv.org/abs/quant-ph/0109094 |
| DOI | 10.1088/0305-4470/34/37/316 |
| Journal | J. Phys. A: Math. Gen. 34 (2001), 7639-7675 |
Abstract
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a possible integral representation of an instrument, which differs from the representations of an instrument available in the mathematical and physical literature. We introduce the notion of a quantum stochastic representation of an instrument, whose elements are wholly determined by the unitary invariants of a measuring process. We show that the description of a generalized direct quantum measurement can be considered in the frame of a new general approach, which we call the quantum stochastic approach (QSA), based on the notion of a family of quantum stochastic evolution operators, satisfying the orthonormality relation and describing the conditional evolution of a quantum system under a measurement. The QSA allows to give: a) the complete statistical description of any generalized direct quantum measurement (a POV measure and a family of posterior states); b) the complete description in a Hilbert space of the stochastic behaviour of a quantum system under a measurement in the sense of specification of the probabilistic transition law governing the change from the initial state of a quantum system to a final one under a single measurement; c) to formalize the consideration of all possible types of quantum measurements. For measurements continuous in time the QSA allows, in particular, to define in the most general case (without assuming any Markov property) the notion of posterior pure state trajectories (quantum trajectories) and to give their probabilistic treatment.
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"abstract": "In the present paper we consider the problem of description of an arbitrary\ngeneralized quantum measurement with outcomes in a measurable space. Analyzing\nthe unitary invariants of a measuring process, we present the most general form\nof a possible integral representation of an instrument, which differs from the\nrepresentations of an instrument available in the mathematical and physical\nliterature. We introduce the notion of a quantum stochastic representation of\nan instrument, whose elements are wholly determined by the unitary invariants\nof a measuring process. We show that the description of a generalized direct\nquantum measurement can be considered in the frame of a new general approach,\nwhich we call the quantum stochastic approach (QSA), based on the notion of a\nfamily of quantum stochastic evolution operators, satisfying the orthonormality\nrelation and describing the conditional evolution of a quantum system under a\nmeasurement. The QSA allows to give: a) the complete statistical description of\nany generalized direct quantum measurement (a POV measure and a family of\nposterior states); b) the complete description in a Hilbert space of the\nstochastic behaviour of a quantum system under a measurement in the sense of\nspecification of the probabilistic transition law governing the change from the\ninitial state of a quantum system to a final one under a single measurement; c)\nto formalize the consideration of all possible types of quantum measurements.\nFor measurements continuous in time the QSA allows, in particular, to define in\nthe most general case (without assuming any Markov property) the notion of\nposterior pure state trajectories (quantum trajectories) and to give their\nprobabilistic treatment.",
"arxiv_id": "quant-ph/0109094",
"authors": [
"Elena R. Loubenets"
],
"categories": [
"quant-ph",
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],
"doi": "10.1088/0305-4470/34/37/316",
"journal_ref": "J. Phys. A: Math. Gen. 34 (2001), 7639-7675",
"title": "Quantum stochastic approach to the description of quantum measurements",
"url": "https://arxiv.org/abs/quant-ph/0109094"
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