Smoothed quantum-classical states in time-irreversible hybrid dynamics

Abstract

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.

arXiv comment10 pages, 4 figures

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Cited by in corpus (9)

• Quantum non-Markovian processes break conditional past-future independence
• Conditional past-future correlation induced by non-Markovian dephasing reservoirs
• Unifying theory of quantum state estimation using past and future information
• Quantum State Smoothing for Linear Gaussian Systems
• Quantum state smoothing: Why the types of observed and unobserved measurements matter
• Entropic relations for retrodicted quantum measurements
• Quantum state smoothing cannot be assumed classical even when the filtering and retrofiltering are classical
• Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation
• A Retrodictive Approach to Quantum State Smoothing