dorsal/arxiv
View SchemaFunctional integral treatment of some quantum nondemolition systems
| Authors | Subhashish Banerjee, R. Ghosh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611127 |
| URL | https://arxiv.org/abs/quant-ph/0611127 |
| DOI | 10.1088/1751-8113/40/6/006 |
| Journal | J. Phys. A: Math. Theo. 40, 1273 (2007) |
Abstract
In the scheme of a quantum nondemolition (QND) measurement, an observable is measured without perturbing its evolution. In the context of studies of decoherence in quantum computing, we examine the `open' quantum system of a two-level atom, or equivalently, a spin-1/2 system, in interaction with quantum reservoirs of either oscillators or spins, under the QND condition of the Hamiltonian of the system commuting with the system-reservoir interaction. For completeness, we also examine the well-known non-QND spin-Bose problem. For all these many-body systems, we use the methods of functional integration to work out the propagators. The propagators for the QND Hamiltonians are shown to be analogous to the squeezing and rotation operators, respectively, for the two kinds of baths considered. Squeezing and rotation being both phase space area-preserving canonical transformations, this brings out an interesting connection between the energy-preserving QND Hamiltonians and the homogeneous linear canonical transformations.
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"abstract": "In the scheme of a quantum nondemolition (QND) measurement, an observable is\nmeasured without perturbing its evolution. In the context of studies of\ndecoherence in quantum computing, we examine the `open\u0027 quantum system of a\ntwo-level atom, or equivalently, a spin-1/2 system, in interaction with quantum\nreservoirs of either oscillators or spins, under the QND condition of the\nHamiltonian of the system commuting with the system-reservoir interaction. For\ncompleteness, we also examine the well-known non-QND spin-Bose problem. For all\nthese many-body systems, we use the methods of functional integration to work\nout the propagators. The propagators for the QND Hamiltonians are shown to be\nanalogous to the squeezing and rotation operators, respectively, for the two\nkinds of baths considered. Squeezing and rotation being both phase space\narea-preserving canonical transformations, this brings out an interesting\nconnection between the energy-preserving QND Hamiltonians and the homogeneous\nlinear canonical transformations.",
"arxiv_id": "quant-ph/0611127",
"authors": [
"Subhashish Banerjee",
"R. Ghosh"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/6/006",
"journal_ref": "J. Phys. A: Math. Theo. 40, 1273 (2007)",
"title": "Functional integral treatment of some quantum nondemolition systems",
"url": "https://arxiv.org/abs/quant-ph/0611127"
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