# Process Products Need Qualification

## TL;DR

This paper identifies a fundamental restriction in the quantum process framework, showing that certain tensor products of processes are invalid, which impacts the understanding of process communication.

## Contribution

It provides a necessary and sufficient condition for when tensor products of quantum processes are valid, revealing a key limitation in the framework.

## Key findings

- Some classical and quantum processes cannot form valid tensor products.
- The paper establishes a precise criterion for process tensor product validity.
- Implications for process communication theory are discussed.

## Abstract

The quantum process framework is devised as a generalization of quantum theory to incorporate indefinite causal structure. In this short paper we point out a restriction in forming products of processes: there exist both classical and quantum processes whose tensor products are not processes. Our main result is a necessary and sufficient condition for when tensor products of multipartite processes are (in)valid. We briefly discuss the implications of this restriction on process communication theory.