Limit theorems for the interference terms of discrete-time quantum walks on the line

TL;DR

This paper derives limit theorems for the off-diagonal elements of the density matrix in discrete-time quantum walks on the line, highlighting their importance in understanding quantum properties beyond position probabilities.

Contribution

It introduces the first limit theorems for the off-diagonal density matrix elements in quantum walks, expanding the analysis beyond traditional probability distributions.

Findings

Limit theorems for off-diagonal density matrix elements

Enhanced understanding of quantum coherence in walks

New tools for quantifying quantumness

Abstract

The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal elements of the density matrix. On the other hand, although off-diagonal parts of the density matrices have an important role to quantify quantumness, they have not received attention in quantum walks. We focus on the off-diagonal parts of the density matrices for discrete-time quantum walks on the line and derive limit theorems for them.