Implementing quantum walks with a single qubit

TL;DR

This paper introduces a simplified method to implement discrete-time quantum walks using only a single qubit, enabling easier experimental realization and detailed study of quantum properties like coherence and correlations.

Contribution

The authors propose a novel one-qubit approach for implementing quantum walks, allowing for straightforward experiments and comprehensive analysis of quantum properties in DTQWs.

Findings

Successfully implemented one- and two-particle DTQWs with seven steps using single photons.

Investigated quantum correlations and coherence in DTQWs with various initial states.

Studied assisted quantum coherence distillation and established bounds for high-dimensional states.

Abstract

Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks (DTQWs) using only a single qubit, in which both coin and walker are encoded in the two-dimensional state space of a single qubit, operations are realized using single-qubit gates only, and high-dimensional final states of DTQWs can be obtained naturally. With this "one-qubit" approach, DTQW experiments can be realized much more easily, compared with previous methods, in most quantum systems and all properties based on quantum states of DTQWs (such as quantum correlation and coherence) can be investigated. By this approach, we experimentally implement one-particle and two-particle DTQWs with seven steps using single photons. Furthermore, we systematically investigate quantum correlations and coherence (based on the full state of the coin and walker) of the DTQW systems with different initial states of the coin, which have not been obtained and studied in DTQW experiments. As an application, we also study the assisted distillation of quantum coherence using the full state of the two-particle DTQW from the experiment. The maximal increase in distillable coherence for high-dimensional mixed states is investigated for the first time by obtaining its upper and lower bounds. Our work opens a new door to implement DTQW experiments and to better explore properties of quantum walks.