dorsal/arxiv
View SchemaQuantum Diffusion, Measurement and Filtering
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510028 |
| URL | https://arxiv.org/abs/quant-ph/0510028 |
| Journal | Probability Theory and its Applications 38 pp 742--757, (1993) and 39 pp 640--658 (1994) |
Abstract
A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative stochastic analysis and integration are outlined. Algebraic differential equations that unify the quantum non Markovian diffusion with continuous non demolition observation are derived. A stochastic equation of quantum diffusion filtering generalising the classical Markov filtering equation to the quantum flows over arbitrary *-algebra is obtained. A Gaussian quantum diffusion with one dimensional continuous observation is considered.The a posteriori quantum state difusion in this case is reduced to a linear quantum stochastic filter equation of Kalman-Bucy type and to the operator Riccati equation for quantum correlations. An example of continuous nondemolition observation of the coordinate of a free quantum particle is considered, describing a continuous collase to the stationary solution of the linear quantum filtering problem found in the paper.
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"abstract": "A brief presentation of the basic concepts in quantum probability theory is\ngiven in comparison to the classical one. The notion of quantum white noise,\nits explicit representation in Fock space, and necessary results of\nnoncommutative stochastic analysis and integration are outlined. Algebraic\ndifferential equations that unify the quantum non Markovian diffusion with\ncontinuous non demolition observation are derived. A stochastic equation of\nquantum diffusion filtering generalising the classical Markov filtering\nequation to the quantum flows over arbitrary *-algebra is obtained. A Gaussian\nquantum diffusion with one dimensional continuous observation is considered.The\na posteriori quantum state difusion in this case is reduced to a linear quantum\nstochastic filter equation of Kalman-Bucy type and to the operator Riccati\nequation for quantum correlations. An example of continuous nondemolition\nobservation of the coordinate of a free quantum particle is considered,\ndescribing a continuous collase to the stationary solution of the linear\nquantum filtering problem found in the paper.",
"arxiv_id": "quant-ph/0510028",
"authors": [
"V. P. Belavkin"
],
"categories": [
"quant-ph",
"math.PR"
],
"journal_ref": "Probability Theory and its Applications 38 pp 742--757, (1993) and\n 39 pp 640--658 (1994)",
"title": "Quantum Diffusion, Measurement and Filtering",
"url": "https://arxiv.org/abs/quant-ph/0510028"
},
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