Experimental demonstration of quantum walks with initial superposition states

TL;DR

This paper demonstrates a linear optics protocol for preparing arbitrary initial superposition states in discrete-time quantum walks, revealing new properties and enabling advanced quantum information applications.

Contribution

It introduces a novel encoding method for arbitrary superposition states in quantum walks and provides the first experimental demonstration of such states using passive linear optics.

Findings

Superposition states affect the spread speed of quantum walks.

Initial superpositions influence entanglement between coin and walker.

The protocol enables encoding high-dimensional quantum states with a single qubit.

Abstract

The preparation of initial superposition states of discrete-time quantum walks (DTQWs) are necessary for the study and applications of DTQWs. In linear optics, it is easy to prepare initial superposition states of the coin, which are always encoded by polarization states; while the preparation of superposition states of the walker is challenging. Based on a novel encoding method, we here propose a DTQW protocol in linear optics which enables the preparation of arbitrary initial superposition states of the walker and the coin. With this protocol, we report an experimental demonstration of DTQW with the walker initially in superposition states, by using only passive linear-optical elements. The effects of the walker's different initial superposition states on the spread speed of the DTQW and on the entanglement between the coin and the walker are also experimentally investigated, which have not been reported before. When the walker starts with superposition states, we show that the properties of DTQW are very different from those of DTQW starting with a single position. Our findings reveal different properties of DTQW and paves an avenue to study DTQW with arbitrary initial states. Moreover, the encoding method enables one to encode an arbitrary high-dimensional quantum state using a single physical qubit and may be adopted to implement other quantum information tasks.