Fundamental limits for realising quantum processes in spacetime

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.

5+6 pages (excluding references). Short version of arXiv:2203.11245 with additional discussions on experiments and spatio-temporal realisations, includes intuitive proof sketch of main results. A cross reference issue present in v1 has been fixed in v2

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• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Circuit locality from relativistic locality in scalar field mediated entanglement
• Distinguishing quantum causal scenarios with indistinguishable classical analogs: The significance of intermediate latents
• Dipole-independent measurements of nearly-zero CMB correlation: a possible symmetry of primordial causal quantum coherence
• Flow of dynamical causal structures with an application to correlations
• Knot invariants and indefinite causal order