How uncertainty enables non-classical dynamics

TL;DR

This paper explores how the quantum uncertainty principle facilitates non-classical dynamics in interferometers, revealing a trade-off that allows quantum theory to maximize non-classical behavior while respecting causality constraints.

Contribution

It demonstrates that the uncertainty principle enables non-classical dynamics in probabilistic theories, and characterizes the trade-off between certainty and non-classicality in quantum mechanics.

Findings

Quantum uncertainty enables non-classical dynamics in interferometers.

Maximal certainty restricts non-classical dynamics to the identity operation.

Quantum theory minimizes certainty to achieve maximal non-classical dynamics.

Abstract

The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance between different paths of an interferometer should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle, that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimises certainty in return for maximal non-classical dynamics.