The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory

Details The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory

2003-07-10

arxiv.org/abs/quant-ph/0307078v3

Phys. Rev. A 68, 062104 (2003)

Physics

Quantum Physics

9 pages

Scientific paper

10.1103/PhysRevA.68.062104

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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