Tensor Universality, Quantum Information Flow, Coecke's Theorem, and Generalizations

TL;DR

This paper demonstrates that Coecke's quantum information flow theorem can be derived from tensor product universality, revealing a PROP structure in multipartite quantum processes and their equivalence to teleportation-like forms.

Contribution

It introduces a new proof of Coecke's theorem using tensor universality and uncovers a PROP structure underlying multipartite quantum information processing.

Findings

Coecke's theorem follows from tensor product universal property.

Multipartite quantum processes are equivalent to a canonical teleportation form.

A PROP structure underpins general quantum information processing.

Abstract

We show that Coecke's compositionality theorem for quantum information flow follows by the universal property of tensor products from the case in which all relevant states are totally disentangled, for which the proof is almost trivial. With the same technique we deduce a PROP structure behind general multipartite quantum information processing and show that all such are equivalent to a canonical teleportation-type form. Some philosophical issues concerning quantum information are also touched upon.