Mixed quantum states in higher categories

TL;DR

This paper proposes a unified categorical framework combining two approaches to classical-quantum interaction, enabling comprehensive descriptions of quantum teleportation and classical encryption with a universal security proof.

Contribution

It introduces a novel integration of two categorical descriptions of classical-quantum interaction, advancing the theoretical understanding and security analysis.

Findings

Unified categorical framework for quantum and classical information

Application to quantum teleportation and classical encryption

Universal security proof for both scenarios

Abstract

There are two ways to describe the interaction between classical and quantum information categorically: one based on completely positive maps between Frobenius algebras, the other using symmetric monoidal 2-categories. This paper makes a first step towards combining the two. The integrated approach allows a unified description of quantum teleportation and classical encryption in a single 2-category, as well as a universal security proof applicable simultaneously to both scenarios.