Non-Markovian channel from the reduced dynamics of coin in quantum walk

TL;DR

This paper characterizes the non-Markovian quantum channel arising from the reduced dynamics of a coin in a discrete-time quantum walk, highlighting its implications for quantum information processing.

Contribution

It introduces a formalism to derive Kraus operators for the non-Markovian channel from quantum walk dynamics and analyzes its properties.

Findings

Non-Markovianity inferred from non-monotonous distinguishability of states.

Characterization of the channel's non-Markovian behavior via P-indivisibility.

Implications for quantum information tasks using such channels.

Abstract

The quantum channels with memory, known as non-Markovian channels, are of crucial importance for a realistic description of a variety of physical systems, and pave ways for new methods of decoherence control by manipulating the properties of environment such as its frequency spectrum. In this work, the reduced dynamics of coin in a discrete-time quantum walk is characterized as a non-Markovian quantum channel. A general formalism is sketched to extract the Kraus operators for a $t$-step quantum walk. Non-Markovianity, in the sense of P-indivisibility of the reduced coin dynamics, is inferred from the non-monotonous behavior of distinguishably of two orthogonal states subjected to it. Further, we study various quantum information theoretic quantities of a qubit under the action of this channel, putting in perspective, the role such channels can play in various quantum information processing tasks.