Composition rules for quantum processes: a no-go theorem

TL;DR

This paper proves a no-go theorem demonstrating that, under basic assumptions, there is no consistent way to compose quantum processes, impacting the development of a Shannon theory for general quantum processes.

Contribution

It establishes a fundamental impossibility result for composing quantum processes, highlighting limitations in resource theories of quantum causality.

Findings

No general composition rule for quantum processes exists.

Implications for quantum Shannon theory and resource management.

Limits the development of a unified framework for quantum causal resources.

Abstract

A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for more general causal structures. Motivated by the interpretation of processes as a resource for quantum information processing shared by two (or more) parties, with advantages recently demonstrated both for computation and communication tasks, we investigate the notion of composition of processes. We show that under very basic assumptions such a composition rule does not exist. While the availability of multiple independent copies of a resource, e.g. quantum states or channels, is the starting point for defining information-theoretic notions such as entropy (both in classical and quantum Shannon theory), our no-go result means that a Shannon theory of general quantum processes will not possess a natural rule for the composition of resources.