Quantum information processing and quantum logic: toward mutual illumination

TL;DR

This paper explores how quantum information and logic can inform the classification of physical theories, aiming to understand quantum mechanics' unique features and inspire new quantum protocols through an axiomatic approach.

Contribution

It proposes using quantum structures and axiomatic methods to analyze and classify physical theories, enhancing understanding of quantum mechanics and guiding the development of novel quantum algorithms.

Findings

Quantum structures help isolate features responsible for quantum advantage.

Axiomatic approaches can classify and compare physical theories.

Understanding system dynamics aids in designing quantum protocols.

Abstract

Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical mechanics. The axiomatic approach of quantum structures may help isolate what aspects of quantum mechanics are responsible for what aspects of its greater-than-classical information processing power, and whether more general physical theories may escape some common limitations of classical and quantum theories. Also, by by helping us understand how existing quantum algorithms work, quantum structures analyses may suggest new quantum protocols exploiting general features of quantum mechanics. I stress the importance, for these matters, of understanding open and closed-system dynamics, and the structure of composite systems in general frameworks for operational theories, such as effect algebras, convex sets, and related structures.