On the entropy of decoherence matrix for quantum walks

TL;DR

This paper calculates the von Neumann entropy of the decoherence matrix in quantum walks, linking it to correlated random walks, thereby advancing understanding of quantum decoherence measures.

Contribution

It introduces a method to compute the entropy of the decoherence matrix using the eigensystem related to correlated random walks, a novel approach in quantum walk analysis.

Findings

Eigenvalues of the decoherence matrix are expressed via correlated random walks.

The von Neumann entropy of the decoherence matrix is explicitly computed.

The approach bridges quantum decoherence and classical stochastic processes.

Abstract

The decoherence matrix studied by Gudder and Sorkin (2011) can be considered as a map from the set of all the pairs of $n$-length paths to complex numbers, which is induced by the discrete-time quantum walk. The decoherence matrix is one of the decoherence functionals which present their historical quantum measure theory. In this paper, we compute the von Neumann entropy of the decoherence matrix. To do so, we use the result that the eigensystem of the decoherence matrix can be expressed by a corresponding correlated random walk.