Abstract Physical Traces

TL;DR

This paper refines the concept of strong compact closure in categorical quantum mechanics, enabling more elegant definitions and better handling of bipartite projectors, thereby advancing the theoretical framework of quantum protocols.

Contribution

It improves the definition of strong compact closure, providing a clearer characterization and enhanced treatment of bipartite projectors in categorical semantics.

Findings

Enhanced definition of strong compact closure

Elegant characterization using adjoints and Yanking axiom

Improved treatment of bipartite projectors

Abstract

We revise our "Physical Traces" paper in the light of the results in "A Categorical Semantics of Quantum Protocols". The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved. In this paper we improve on the definition of strong compact closure as compared to the one presented in Categorical Semantics of Quantum Protocols. This modification enables an elegant characterization of strong compact closure in terms of adjoints and a Yanking axiom, and a better treatment of bipartite projectors.