Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization

Abstract

A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but much less is known beyond this regime. Here we propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map. The idea is to replace its unphysical Choi operator with its closest physical one, mimicking recent work on quantum process tomography. We also show that the regularized dynamics is more accurate in terms of reproducing the exact dynamics: this allows to heuristically push the utilization of these master equations in moderate coupling regimes, where the loss of positivity can have relevant impact.

12 pages, 5 figures. Close to published version

References in corpus (16)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Preservation of Positivity by Dynamical Coarse-Graining
• Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• A thermodynamically consistent Markovian master equation beyond the secular approximation
• Lindbladian approximation beyond ultra-weak coupling
• Thermodynamic consistency of quantum master equations
• Projected Least-Squares Quantum Process Tomography
• Simple master equations for describing driven systems subject to classical non-Markovian noise
• Searching for Lindbladians obeying local conservation laws and showing thermalization
• Geometric-Arithmetic Master Equation in Large and Fast Open Quantum Systems
• A time-dependent regularization of the Redfield equation
• Local generation of entanglement with Redfield dynamics

Cited by in corpus (2)

• Unifying quantum stochastic methods using Wick's theorem on the Keldysh contour
• Electron dynamics induced by quantum cat-state light