A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem

TL;DR

This paper employs 2-categorical methods to analyze quantum procedures, demonstrating the equivalence of complementary measurements and quantum key distribution, and providing a categorical solution to the Mean King problem.

Contribution

It introduces a 2-categorical framework for describing quantum structures, establishing their equivalence and solving the Mean King problem abstractly.

Findings

Complementary measurements and quantum key distribution are shown to be equivalent.

A 2-categorical formulation of the Mean King problem is provided.

The framework offers a new perspective on quantum procedures using category theory.

Abstract

This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that they are equivalent. We then show abstractly that either structure gives a solution to the Mean King problem, which we also formulate 2-categorically.