Information backflow may not indicate quantum memory

Understand

We analyze recent approaches to quantum Markovianity and how they relate to the proper definition of quantum memory.

• We point out that the well-known criterion of information backflow may not correctly report character of the memory falsely signaling its quantumness.
• Therefore, as a complement to the well-known criteria, we propose several concepts of elementary dynamical maps.
• Maps of this type do not increase distinguishability of states which are indistinguishable by von Neumann measurements in a given basis.