Deriving Dagger Compactness

TL;DR

This paper derives dagger compactness from operational axioms in categories with mixed states and purification, clarifying its interpretation in physical process theories.

Contribution

It provides a new derivation of dagger compactness from operational principles, linking it to quantum-like structures.

Findings

Dagger compactness characterized via a 'state dagger' mapping

Derived in categories with 'completely mixed' states and purification

Clarifies the interpretation of dagger compactness in physical theories

Abstract

Dagger compact structure is a common assumption in the study of physical process theories, but lacks a clear interpretation. Here we derive dagger compactness from more operational axioms on a category. We first characterise the structure in terms of a simple mapping of states to effects which we call a 'state dagger', before deriving this in any category with 'completely mixed' states and a form of purification, as in quantum theory.