Stochastic entropy production for continuous measurements of an open quantum system

Abstract

We investigate the total stochastic entropy production of a two-level bosonic open quantum system under protocols of time dependent coupling to a harmonic environment. These processes are intended to represent the measurement of a system observable, and consequent selection of an eigenstate, whilst the system is also subjected to thermalising environmental noise. The entropy production depends on the evolution of the system variables and their probability density function, and is expressed through system and environmental contributions. The continuous stochastic dynamics of the open system is based on the Markovian approximation to the exact, noise-averaged stochastic Liouville-von Neumann equation, unravelled through the addition of stochastic environmental disturbance mimicking a measuring device. Under the thermalising influence of time independent coupling to the environment, the mean rate of entropy production vanishes asymptotically, indicating equilibrium. In contrast, a positive mean production of entropy as the system responds to time dependent coupling characterises the irreversibility of quantum measurement, and a comparison of its production for two coupling protocols, representing connection to and disconnection from the external measuring device, satisfies a detailed fluctuation theorem.

25 pages, 7 figures

References in corpus (10)

• A Straightforward Introduction to Continuous Quantum Measurement
• Fluctuation theorems for stochastic dynamics
• The role of quantum measurement in stochastic thermodynamics
• Genuine quantum trajectories for non-Markovian processes
• Quantum Operation Time Reversal
• Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
• Non-perturbative stochastic method for driven spin-boson model
• Partition-free approach to open quantum systems in harmonic environments: an exact stochastic Liouville equation
• Efficient choice of coloured noises in stochastic dynamics of open quantum systems
• Exactly Thermalised Quantum Dynamics of the Spin-Boson Model coupled to a Dissipative Environment

Cited by in corpus (4)

• Stochastic quantum trajectories demonstrate the Quantum Zeno Effect in open spin 1/2, spin 1 and spin 3/2 systems
• Memory effects in a sequence of measurements of non-commuting observables
• Stochastic entropy production associated with quantum measurement in a framework of Markovian quantum state diffusion
• Characterising quantum measurement through environmental stochastic entropy production in a two spin 1/2 system