Quantum evolution with a large number of negative decoherence rates

TL;DR

This paper demonstrates that non-Markovian quantum evolution with many negative decoherence rates can originate from simple mixtures of Markovian processes, challenging traditional assumptions about positivity and memory effects.

Contribution

It shows that non-Markovian dynamics with numerous negative rates are possible from mixtures of Markovian semigroups, expanding understanding of quantum memory effects.

Findings

Negative decoherence rates can arise from simple mixtures of Markovian processes.

Up to (d-1)^2 negative rates are possible in a d-dimensional quantum system.

Quantum evolution remains valid despite multiple negative rates.

Abstract

Non-Markovian effects in quantum evolution appear when the system is strongly coupled to the environment and interacts with it for long periods of time. To include memory effects in the master equations, one usually incorporates time-local generators or memory kernels. However, it turns out that non-Markovian evolution with eternally negative decoherence rates arises from a simple mixture of Markovian semigroups. Moreover, one can have as many as $(d-1)^2$ always negative rates out of $d^2-1$ total, and the quantum evolution is still legitimate.