Guess Your Neighbour’s Input: No Quantum Advantage but an Advantage for Quantum Theory

Abstract

Quantum mechanics dramatically differs from classical physics. An interesting consequence of this fact is that quantum resources offer an advantage over classical resources in many information-theoretic tasks. In quantum information, the goal of which is to understand information processing from a quantum perspective, 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? In this review we focus on a simple information-theoretic game called ‘guess your neighbour’s input’, for which classical and quantum players perform equally well. Interestingly, 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.