Quantum dynamical maps and Markovianity

TL;DR

This paper investigates the conditions under which the intermediate dynamics of a quantum subsystem are completely positive, revealing insights into the nature of Markovian and non-Markovian quantum processes without relying on master equations.

Contribution

It demonstrates that intermediate quantum dynamical maps are not necessarily completely positive, clarifying the distinction between Markovian and non-Markovian dynamics based on system-environment interactions.

Findings

Intermediate dynamics may not be CP, even if initial and final states are CP.

Markovianity is linked to CP intermediate maps, non-Markovianity to NCP.

The results are derived without using the master equation approach.

Abstract

It is known that the time evolution of a subsystem from an initial state to two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is shown here that in the intermediate times between t1 and t2, in general, it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if NCP) avataras of the intermediate dynamics. This is brought out based on A and B dynamical maps - without resorting to Master equation approach. The choice of tensor product form for the global initial state points towards the system-environment interaction dynamics as the sole cause for Markovianity/non-Markovianity. A succinct summary of the results is given in the form of a table.