Completely positive classical structures and sequentializable quantum protocols

TL;DR

This paper explores classical structures in categories of completely positive morphisms and demonstrates that quantum maps with commuting Kraus operators can be sequentialized, showing robustness under dephasing noise.

Contribution

It introduces a framework for classical structures across various categories and proves the sequentializability of certain quantum maps, advancing understanding of quantum protocol robustness.

Findings

Quantum maps with commuting Kraus operators can be sequentialized.

Protocols are equally robust under dephasing noise whether entangled or sequential.

Classical structures are characterized in multiple categorical settings.

Abstract

We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with commuting Kraus operators can be sequentialized. Hence such protocols are precisely as robust under general dephasing noise when entangled as when sequential.