# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.05172