How uncertainty enables 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.

4 pages + 4 page technical supplement, 2 figures

References in corpus (7)

• The uncertainty principle determines the non-locality of quantum mechanics
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Information Invariance and Quantum Probabilities
• A violation of the uncertainty principle implies a violation of the second law of thermodynamics
• A general framework for phase and interference
• Popescu-Rohrlich Boxes in Quantum Measure Theory

Cited by in corpus (13)

• General probabilistic theories: An introduction
• A general framework for phase and interference
• Gouy phase in non-classical paths in triple-slit interference experiment
• Interferometric computation beyond quantum theory
• The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer
• On defining the Hamiltonian beyond quantum theory
• Unification of energy concepts in generalised phase space theories
• Orthogonal-state-based cryptography in quantum mechanics and local post-quantum theories
• From reasonable postulates to generalised Hamiltonian systems
• Quantum Darwinism and the spreading of classical information in non-classical theories
• On the origin of nonclassicality in single systems
• Estimation independence as an axiom for quantum uncertainty
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories