Causality in Pure Quantum Computation with Quantum Control

2026-07-17

AI Summary

This work proposes a typed lambda calculus with quantum control to rule out physically unrealizable higher-order quantum processes exhibiting indefinite causal order, such as the OCB process. The type system is grounded in intuitionistic BV logic, marking the first integration of BV logic with quantum control to enforce causal constraints at the linguistic level. A corresponding categorical semantics is developed, closely aligned with the Caus construction, thereby formally guaranteeing physical realizability. Theoretical analysis demonstrates that the proposed system inherently excludes known non-causal processes, embedding causality directly into the language’s expressive structure.

Abstract

Indefinite causal order is a characteristic phenomenon in quantum computation, with examples including the quantum SWITCH and the OCB process. Not all such processes are believed to be physically realizable: while some implementations of the quantum SWITCH have been proposed, the OCB process is suspected to be unrealizable. This difference in realizability is commonly attributed to constraints imposed by physical causality. This paper studies such a causality issue in a higher-order setting, proposing a typed lambda calculus with quantum control and its categorical semantics. Our calculus extends pure quantum computation with higher-order functions and quantum conditional branching, and it is equipped with a type system based on intuitionistic BV logic to enforce causality. We also present a novel model that is closely related to the Caus construction, by which we prove that some physically-unrealizable processes are not definable in our language.

Problem

• causality
• indefinite causal order
• quantum computation
• higher-order processes
• physical realizability

Innovation

• indefinite causal order
• quantum control
• typed lambda calculus
• intuitionistic BV logic
• Caus construction