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

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.

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• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
• Open system approach to Neutrino oscillations in a quantum walk framework
• Designing three-way entangled and nonlocal two-way entangled single particle states via alternate quantum walks
• On the eternal non-Markovianity of non-unital quantum channels
• On the non-Markovianity of quantum semi-Markov processes
• Quantum walks under superposition of causal order