Duality games and operational duality relations

TL;DR

This paper provides an operational interpretation of wave-particle duality through discrimination games involving interferometry, establishing duality as a constraint on winning probabilities and deriving a tight duality relation.

Contribution

It introduces a novel game-based framework to quantify wave-particle duality and derives a tight duality relation linking game success probabilities.

Findings

Derived a tight wave-particle duality relation.

Established an upper bound on combined game success probabilities.

Connected wave-particle duality to discrimination game outcomes.

Abstract

We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3 parties, Alice and Bob, who cooperate, and the House, who supervises the game. In one game called ways they attempt to determine the path of a particle in the interferometer. In another, called phases, they attempt to determine which set of known phases have been applied to the different paths. The House determines which game is to be played by flipping a coin. We find a tight wave-particle duality relation that allows us to relate the probabilities of winning these games, and use it to find an upper bound on the probability of winning the combined game. This procedure allows us to describe wave-particle duality in terms of discrimination probabilities.