Mr. Jay M. Gambetta Profile

Jay M. Gambetta

at Griffith Univ

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Proceedings Article | 16 May 2003 Paper

A non-Markovian stochastic Schrödinger equation developed from a hidden variable interpretation

Jay Gambetta, Howard Wiseman

Proceedings Volume 5111, (2003) https://doi.org/10.1117/12.496938

KEYWORDS: Stochastic processes, Quantum mechanics, Homodyne detection, Fluctuations and noise, Photonics, Quantum optics, Time metrology, Environmental sensing, Pollution control, Mechanics

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Do non-Markovian diffusive stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE at time t 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 show that such trajectories be interpreted using a non-standard interpretation of quantum mechanics, namely hidden variables theory. The simplest example is a non-Markovian SSE, which we call a position unraveling, which results from a description of the bath using Bohmian mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a weighted sum of trajectories for the positions of the bath modes. The solution of the non-Markovian SSE is the state of the system 'conditioned' on values of the bath positions. It also determines the guiding wave for these positions. We also discuss previously used unravelings which have the Markovian limits of homodyne and heterodyne detection.

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