Stochastic entropy production associated with quantum measurement in a
framework of Markovian quantum state diffusion
- URL: http://arxiv.org/abs/2301.08197v1
- Date: Thu, 19 Jan 2023 17:47:39 GMT
- Title: Stochastic entropy production associated with quantum measurement in a
framework of Markovian quantum state diffusion
- Authors: Claudia L. Clarke and Ian J. Ford
- Abstract summary: We investigate a two level open quantum system using a framework of quantum state diffusion.
We consider the unpredictability of its reduced density matrix when subjected to an environment-driven process of continuous quantum measurement.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The reduced density matrix that characterises the state of an open quantum
system is a projection from the full density matrix of the quantum system and
its environment, and there are many full density matrices consistent with a
given reduced version. Without a specification of relevant details of the
environment, the evolution of a reduced density matrix is therefore typically
unpredictable, even if the dynamics are deterministic. With this in mind, we
investigate a two level open quantum system using a framework of quantum state
diffusion. We consider the pseudorandom evolution of its reduced density matrix
when subjected to an environment-driven process of continuous quantum
measurement of a system observable, using dynamics that asymptotically send the
system to an eigenstate. The unpredictability is characterised by a stochastic
entropy production, the average of which corresponds to an increase in the
subjective uncertainty of the quantum state adopted by the system and
environment, given the underspecified dynamics. This differs from a change in
von Neumann entropy, and can continue indefinitely as the system is guided
towards an eigenstate. As one would expect, the simultaneous measurement of two
non-commuting observables within the same framework does not send the system to
an eigenstate. Instead, the probability density function describing the reduced
density matrix of the system becomes stationary over a continuum of pure
states, a situation characterised by zero further stochastic entropy
production. Transitions between such stationary states, brought about by
changes in the relative strengths of the two measurement processes, give rise
to finite positive mean stochastic entropy production. The framework
investigated can offer useful perspectives on both the dynamics and
irreversible thermodynamics of measurement in quantum systems.
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