Thermodynamic and steady-state implications of Choi-proximity regularization

Determine the implications of Choi-proximity regularization—the Frobenius-norm projection of an unphysical Choi operator onto the set of physical Choi operators corresponding to trace-preserving completely positive channels—for the thermodynamics of open quantum systems and for the structure of the steady-state manifold of the regularized dynamics.

Background

The paper introduces Choi-proximity regularization, a numerical procedure that projects an unphysical Choi operator onto the convex set of physical Choi operators (associated with completely positive, trace-preserving channels), thereby producing a regularized dynamical map that is guaranteed to be CPT while remaining close to the original map. The authors show that this projection improves accuracy relative to the exact dynamics and can retain non-Markovian features without imposing additional Markovian assumptions.

The formal master equations derived for the regularized dynamics reveal an explicit dependence on the initial state and indicate potential changes in non-Markovian behavior relative to the original evolution. Despite these practical advantages, the authors note that they have not provided a clear physical interpretation of the regularized dynamics and explicitly identify understanding its implications for thermodynamics and steady-state structure as an open problem.