On admissible memory kernels for random unitary qubit evolution

TL;DR

This paper investigates conditions under which memory kernels produce legitimate quantum evolutions for qubits, recovering known models and discovering new classes, while revealing surprising non-Markovianity properties.

Contribution

It provides sufficient conditions for physically valid memory kernels in qubit evolution and introduces new classes of nontrivial quantum dynamics.

Findings

Recovered several well-known qubit evolution models

Generated new classes of nontrivial qubit evolutions

Found that certain memory kernels lead to zero non-Markovianity measure

Abstract

We analyze random unitary evolution of the qubit within memory kernel approach. We provide sufficient conditions which guarantee that the corresponding memory kernel generates physically legitimate quantum evolution. Interestingly, we are able to recover several well known examples and generate new classes of nontrivial qubit evolution. Surprisingly, it turns out that quantum evolution with memory kernel generated by our approach gives rise to vanishing non-Markovianity measure based on the distinguishability of quantum states.