Non-Markovian random unitary qubit dynamics

• Random unitary dynamics of a qubit is considered.
• We formulate necessary and sufficient condition for the evolution to be Markovian.
• We derive simple conditions which guarantee that the evolution provides negative information flow.
• As a byproduct it is shown that entropy might monotonically increase even for non-Markovian qubit dynamics.

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.