Partial particle and wave information and weak duality games

TL;DR

This paper explores duality games based on wave-particle duality, demonstrating conditions where players can always win by analyzing partial information and developing a mutual information-based duality relation.

Contribution

It introduces a framework for duality games involving partial wave and particle information and derives a wave-particle duality relation using mutual information.

Findings

Players can always win when partial information is limited.

A mutual information-based duality relation is established.

Examples of duality games with guaranteed winning strategies.

Abstract

Duality games are a way of looking at wave-particle duality. In these games. Alice and Bob together are playing against the House. The House specifies, at random, which of two sub-games Alice and Bob will play. One game, Ways, requires that they obtain path information about a particle going through an $N$-path interferometer and the other, Phases, requires that they obtain phase information. In general, because of wave-particle duality, Alice and Bob cannot always win the overall game. However, if the required amount of path and phase information is not too great, for example specifying a set of paths or phases, one of which is the right one, then they can always win. Here we study examples of duality games that can always be won, and develop a wave-particle duality relation expressed only in terms of mutual information to help analyze these games.