dorsal/arxiv
View SchemaThe interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory
| Authors | Jay Gambetta, H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307078 |
| URL | https://arxiv.org/abs/quant-ph/0307078 |
| DOI | 10.1103/PhysRevA.68.062104 |
| Journal | Phys. Rev. A 68, 062104 (2003) |
Abstract
Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function $z(t)$ appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value $z(t)$ even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system ``conditioned'' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.
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"abstract": "Do diffusive non-Markovian stochastic Schr\\\"odinger equations (SSEs) for open\nquantum systems have a physical interpretation? In a recent paper [Phys. Rev. A\n66, 012108 (2002)] we investigated this question using the orthodox\ninterpretation of quantum mechanics. We found that the solution of a\nnon-Markovian SSE represents the state the system would be in at that time if a\nmeasurement was performed on the environment at that time, and yielded a\nparticular result. However, the linking of solutions at different times to make\na trajectory is, we concluded, a fiction. In this paper we investigate this\nquestion using the modal (hidden variable) interpretation of quantum mechanics.\nWe find that the noise function $z(t)$ appearing in the non-Markovian SSE can\nbe interpreted as a hidden variable for the environment. That is, some chosen\nproperty (beable) of the environment has a definite value $z(t)$ even in the\nabsence of measurement on the environment. The non-Markovian SSE gives the\nevolution of the state of the system ``conditioned\u0027\u0027 on this environment hidden\nvariable. We present the theory for diffusive non-Markovian SSEs that have as\ntheir Markovian limit SSEs corresponding to homodyne and heterodyne detection,\nas well as one which has no Markovian limit.",
"arxiv_id": "quant-ph/0307078",
"authors": [
"Jay Gambetta",
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.062104",
"journal_ref": "Phys. Rev. A 68, 062104 (2003)",
"title": "The interpretation of non-Markovian stochastic Schr\\\"odinger equations as a hidden-variable theory",
"url": "https://arxiv.org/abs/quant-ph/0307078"
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