Entropy analysis of the discrete-time quantum walk under bit-flip noise channel

Abstract

We study the behavior of tunable one-dimensional discrete-time quantum walk (DTQW) in the presence of decoherence modeled by the flip-bit noise channel. By varying the noise intensity, we obtain a wide range of probability distributions of noisy walks, which can be loosely characterized as pure quantum walk, quantum-like walk, semi-classical like walk, and classical-like walk. We show the maximum Shannon entropy of the walk is not obtained under maximum decoherence, but instead at a lower degree of decoherence. This result may be useful for the implementation of quantum error correction, quantum cryptography, and quantum communication protocol, where one might expect the qubit internal state to be flipped due to noise.