Relaxed uncertainty relations and information processing

TL;DR

This paper explores theories that relax quantum uncertainty relations, leading to stronger non-local correlations, improved information encoding, but increased difficulty in state learning, highlighting fundamental differences from quantum mechanics.

Contribution

It demonstrates how relaxing uncertainty relations results in stronger non-locality, superstrong encodings, and altered state learnability, expanding understanding of non-quantum non-signaling theories.

Findings

Tsirelson's bound derived from the uncertainty relation

Relaxed relations enable stronger non-local correlations

Superstrong random access encodings and exponential communication savings

Abstract

We consider a range of "theories" that violate the uncertainty relation for anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty relation, and that relaxing this relation allows for non-local correlations that are stronger than what can be obtained in quantum mechanics. We continue to construct a hierarchy of related non-signaling theories, and show that on one hand they admit superstrong random access encodings and exponential savings for a particular communication problem, while on the other hand it becomes much harder in these theories to learn a state. We show that the existence of these effects stems from the absence of certain constraints on the expectation values of commuting measurements from our non-signaling theories that are present in quantum theory.