Process Products Need Qualification

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.

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References in corpus (6)

• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
• Witnessing causal nonseparability
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Cited by in corpus (11)

• Cyclic Quantum Causal Models
• On the definition and characterisation of multipartite causal (non)separability
• Causal order as a resource for quantum communication
• Quantum Causal Influence
• Quantum superpositions of causal orders as an operational resource
• Classical communication through quantum causal structures
• Composition rules for quantum processes: a no-go theorem
• Quantum from principles without assuming definite causal structure
• Revisiting dynamics of quantum causal structures -- when can causal order evolve?
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Comparative analysis of robust entanglement generation in engineered XX spin chains