Fundamental limits for realising quantum processes in spacetime

TL;DR

This paper establishes fundamental no-go theorems constraining the realization of quantum processes, including indefinite causal order, within classical spacetime frameworks, reconciling quantum and relativistic causality principles.

Contribution

It derives new no-go theorems that limit how quantum processes, especially those with indefinite causal order, can be implemented in classical spacetimes, providing a unified causality framework.

Findings

ICO processes require non-localization in spacetime for realization

Any ICO process can be described with a definite causal order

Results apply to experimental realizations like the quantum switch

Abstract

Understanding the interface between quantum and relativistic theories is crucial for fundamental and practical advances, especially given that key physical concepts such as causality take different forms in these theories. Bell's no-go theorem reveals limits on classical processes, arising from relativistic causality principles. Considering whether similar fundamental limits exist on quantum processes, we derive no-go theorems for quantum experiments realisable in classical background spacetimes. We account for general processes allowed by quantum theory, including those with indefinite causal order (ICO), which have also been the subject of recent experiments. Our first theorem implies that realisations of ICO processes that do not violate relativistic causality must involve the non-localization of systems in spacetime. The second theorem shows that for any such realisation of an ICO process, there exists a more fine-grained description in terms of a definite and acyclic causal order process. This enables a general reconciliation of quantum and relativistic notions of causality and, in particular, applies to experimental realisations of the quantum switch, a prominent ICO process. By showing what is impossible to achieve in classical spacetimes, these no-go results also offer insights into how causality and information processing may differ in future quantum experiments in relativistic regimes beyond classical spacetimes.