dorsal/arxiv
View SchemaQuantum Noise, Bits and Jumps: Uncertainties, Decoherence, Trajectories and Filtering
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512208 |
| URL | https://arxiv.org/abs/quant-ph/0512208 |
| Journal | Progress in Quantum Electronics 25 (2001) No 1, 1 - 53 |
Abstract
It is shown that many dissipative phenomena of "old" quantum mechanics which appeared 100 years ago in the form of the statistics of quantum thermal noise and quantum spontaneous jumps, have never been explained by the "new" conservative quantum mechanics discovered 75 years ago by Heisenberg and Schroedinger. This led to numerous quantum paradoxes which are reconsidered in this paper. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators from the algebra of the actual observables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of past observables with the potential future. This rule, together with the self-compatibility of measurements insuring the consistency of histories, is called the nondemolition principle. The application of this causality condition in the form of the dynamical commutation relations leads to the derivation of the generalized von Neumann reductions, usharp, instantaneous, spontaneous, and even continuous in time. This gives a quantum probabilistic solution, in the form of the dynamical filtering equations, of the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting with Schroedinger and Bohr. The simplest Markovian quantum stochastic model for the continuous in time measurements involves a boundary-value problem in second quantization for input "offer" waves in one extra dimension, and a reduction of the algebra of "actual" observables to an Abelian subalgebra for the output waves.
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"abstract": "It is shown that many dissipative phenomena of \"old\" quantum mechanics which\nappeared 100 years ago in the form of the statistics of quantum thermal noise\nand quantum spontaneous jumps, have never been explained by the \"new\"\nconservative quantum mechanics discovered 75 years ago by Heisenberg and\nSchroedinger. This led to numerous quantum paradoxes which are reconsidered in\nthis paper. The development of quantum measurement theory, initiated by von\nNeumann, indicated a possibility for resolution of this interpretational crisis\nby divorcing the algebra of the dynamical generators from the algebra of the\nactual observables. It is shown that within this approach quantum causality can\nbe rehabilitated in the form of a superselection rule for compatibility of past\nobservables with the potential future. This rule, together with the\nself-compatibility of measurements insuring the consistency of histories, is\ncalled the nondemolition principle. The application of this causality condition\nin the form of the dynamical commutation relations leads to the derivation of\nthe generalized von Neumann reductions, usharp, instantaneous, spontaneous, and\neven continuous in time. This gives a quantum probabilistic solution, in the\nform of the dynamical filtering equations, of the notorious measurement problem\nwhich was tackled unsuccessfully by many famous physicists starting with\nSchroedinger and Bohr. The simplest Markovian quantum stochastic model for the\ncontinuous in time measurements involves a boundary-value problem in second\nquantization for input \"offer\" waves in one extra dimension, and a reduction of\nthe algebra of \"actual\" observables to an Abelian subalgebra for the output\nwaves.",
"arxiv_id": "quant-ph/0512208",
"authors": [
"V. P. Belavkin"
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"journal_ref": "Progress in Quantum Electronics 25 (2001) No 1, 1 - 53",
"title": "Quantum Noise, Bits and Jumps: Uncertainties, Decoherence, Trajectories and Filtering",
"url": "https://arxiv.org/abs/quant-ph/0512208"
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