Parallel repetition of local simultaneous state discrimination

TL;DR

This paper investigates the advantage of no-signalling strategies over classical strategies in local simultaneous state discrimination, showing that no-signalling strategies can outperform classical ones in certain multi-instance scenarios, especially with list-decoding schemes.

Contribution

It introduces a new analysis of no-signalling versus classical strategies in LSSD, demonstrating their potential advantage and extending the framework to general channels using coding theory.

Findings

No-signalling strategies do not outperform classical ones for three players with binary values.

No-signalling strategies outperform classical strategies in multi-instance games based on binary symmetric channels.

List-decoding schemes achieve the asymptotic limit of the classical winning probability exponent.

Abstract

Local simultaneous state discrimination (LSSD) is a recently introduced problem in quantum information processing. Its classical version is a non-local game played by non-communicating players against a referee. Based on a known probability distribution, the referee generates one input for each of the players and keeps one secret value. The players have to guess the referee's value and win if they all do so. For this game, we investigate the advantage of no-signalling strategies over classical ones. We show numerically that for three players and binary values, no-signalling strategies cannot provide any improvement over classical ones. For a certain LSSD game based on a binary symmetric channel, we show that no-signalling strategies are strictly better when multiple simultaneous instances of the game are played. Good classical strategies for this game can be defined by codes, and good no-signalling strategies by list-decoding schemes. We expand this example game to a class of games defined by an arbitrary channel, and extend the idea of using codes and list decoding to define strategies for multiple simultaneous instances of these games. Finally, we give an expression for the limit of the exponent of the classical winning probability, and show that no-signalling strategies based on list-decoding schemes achieve this limit.