#### IMSc Webinar

#### Aspects of non-Markovianity in open quantum system dynamics and quantum communication

#### Shrikant U

##### Poornaprajna Institute of Scientific Research (PPISR), Bengaluru

*meet.google.com/vme-uunm-rdm*

In this talk, I will introduce a new measure of non-Markovianity based on the causality measure - a measure of temporalness of quantum correlations - arising out of pseudo-density matrix formalism. I will present a couple of interesting results pertaining to the existence and elimination of singularities of Pauli channels under convex combinations. I will present how non-unital nature of quantum channels helps in a specific quantum key distribution protocol for a specific attack and how non-Markovianity may give a boost to the advantage due to non-unitality. I will introduce a method to obtain non-Markovian analogues of dephasing and general Pauli channels whose non-Markovianity is solely characterized by singularities in the time-local generator. These channels are shown to be quasi-eternally non-Markovian for a range of non-Markovianity parameter. I shall present a novel concept of Markovianity, namely temporal self-similarity of dynamical maps, which reinstates the well-known definition based on semigroup evolution, and give some examples of processes which are completely positive divisible but possess memory in the sense that they deviate from TSS or semigroup evolution. A measure of the deviation is proposed based on the time-averaged distance between time-dependent and time-independent Linblad evolutions.

References:

1. SU, Quantum causal correlations and non-Markovianity of quantum evolution, Phys. Lett. A, 386, 126983 (2021).

2. SU, V. N. Rao, R. Srikanth, S. Banerjee, Singularities, mixing, and non-Markovianity of Pauli dynamical maps, [To appear in] Phys. Rev. A., 00, 002600 (2021).

3. SU, V. N. Rao, R. Srikanth, S. Banerjee, A class of quasi-eternal non-Markovian channels and their measure, [To appear in] Open. Sys. Inf. Dyn. (2021).

4. SU, R. Srikanth, S. Banerjee, Non-Markovian dephasing and depolarizing channels, Phys. Rev. A, 98, 032328 (2018).

5. SU, R. Srikanth, S. Banerjee, Ping-pong quantum key distribution with trusted noise: non-Markovian advantage, Quantum Inf. Process. 19, 366 (2020).

6. SU, R. Srikanth, S. Banerjee, Temporal self-similarity of quantum dynamical maps as a concept of memorylessness, Sci. Rep.10, 1 (2020).

Done