Guess your neighbour's input: no quantum advantage but an advantage for quantum theory

TL;DR

This paper analyzes a simple information game showing no quantum advantage over classical strategies, yet revealing fundamental differences between quantum mechanics and more general theories, with implications for quantum foundations and information theory.

Contribution

It introduces and studies the 'guess your neighbour's input' game, highlighting its role in distinguishing quantum mechanics from broader physical theories.

Findings

Classical and quantum players perform equally in the game.

The game helps differentiate quantum mechanics from more general theories.

Applications relate to Gleason's theorem and entanglement bounds.

Abstract

Quantum mechanics dramatically differs from classical physics, allowing for a wide range of genuinely quantum phenomena. The goal of quantum information is to understand information processing from a quantum perspective. In this mindset, it is thus natural to focus on tasks where quantum resources provide an advantage over classical ones, and to overlook tasks where quantum mechanics provides no advantage. But are the latter tasks really useless from a more general perspective? Here we discuss a simple information-theoretic game called 'guess your neighbour's input', for which classical and quantum players perform equally well. We will see that this seemingly innocuous game turns out to be useful in various contexts. From a fundamental point of view, the game provides a sharp separation between quantum mechanics and other more general physical theories, hence bringing a deeper understanding of the foundations of quantum mechanics. The game also finds unexpected applications in quantum foundations and quantum information theory, related to Gleason's theorem, and to bound entanglement and unextendible product bases.