dorsal/arxiv
View SchemaNon-Markovian stochastic Schr\"odinger equations: Generalization to real-valued noise using quantum measurement theory
| Authors | Jay Gambetta, H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202117 |
| URL | https://arxiv.org/abs/quant-ph/0202117 |
| DOI | 10.1103/PhysRevA.66.012108 |
| Journal | Phys. Rev. A 66, 012108 (2002) |
Abstract
Do stochastic Schr\"odinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system {\em on average} obeys a master equation, the answer is yes. Markovian stochastic Schr\"odinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic \sch equation introduced by Strunz, Di\' osi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement theory approach, we rederive their unraveling which involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection respectively. Although we use quantum measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.
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"abstract": "Do stochastic Schr\\\"odinger equations, also known as unravelings, have a\nphysical interpretation? In the Markovian limit, where the system {\\em on\naverage} obeys a master equation, the answer is yes. Markovian stochastic\nSchr\\\"odinger equations generate quantum trajectories for the system state\nconditioned on continuously monitoring the bath. For a given master equation,\nthere are many different unravelings, corresponding to different sorts of\nmeasurement on the bath. In this paper we address the non-Markovian case, and\nin particular the sort of stochastic \\sch equation introduced by Strunz, Di\\\u0027\nosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement\ntheory approach, we rederive their unraveling which involves complex-valued\nGaussian noise. We also derive an unraveling involving real-valued Gaussian\nnoise. We show that in the Markovian limit, these two unravelings correspond to\nheterodyne and homodyne detection respectively. Although we use quantum\nmeasurement theory to define these unravelings, we conclude that the stochastic\nevolution of the system state is not a true quantum trajectory, as the identity\nof the state through time is a fiction.",
"arxiv_id": "quant-ph/0202117",
"authors": [
"Jay Gambetta",
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.012108",
"journal_ref": "Phys. Rev. A 66, 012108 (2002)",
"title": "Non-Markovian stochastic Schr\\\"odinger equations: Generalization to real-valued noise using quantum measurement theory",
"url": "https://arxiv.org/abs/quant-ph/0202117"
},
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