Quantum theory cannot violate a causal inequality

Abstract

Within quantum theory, we can create superpositions of different causal orders of events, and observe interference between them. This raises the question of whether quantum theory can produce results that would be impossible to replicate with any classical causal model, thereby violating a causal inequality. This would be a temporal analogue of Bell inequality violation, which proves that no local hidden variable model can replicate quantum results. However, unlike the case of non-locality, we show that quantum experiments \emph{can} be simulated by a classical causal model, and therefore cannot violate a causal inequality.

arXiv comment16 pages, 2 figures

References in corpus (22)

• Quantum correlations with no causal order
• Quantum computations without definite causal structure
• Experimental Superposition of Orders of Quantum Gates
• Computational advantage from quantum-controlled ordering of gates
• Enhanced communication with the assistance of indefinite causal order
• Perfect discrimination of no-signalling channels via quantum superposition of causal structures
• Indefinite Causal Order in a Quantum Switch
• Guess your neighbour's input: a multipartite non-local game with no quantum advantage
• Witnessing causal nonseparability
• Causal and causally separable processes
• Bell's Theorem for Temporal Order
• The simplest causal inequalities and their violation
• Quantum computation with programmable connections between gates
• Adaptive versus non-adaptive strategies for quantum channel discrimination
• Constraints on nonlocality in networks from no-signaling and independence
• Multipartite Causal Correlations: Polytopes and Inequalities
• Cyclic Quantum Causal Models
• Quantum computation with indefinite causal structures
• Experiments on quantum causality
• Witnesses of causal nonseparability: an introduction and a few case studies
• Consequences of preserving reversibility in quantum superchannels
• Quantum chicken-egg dilemmas: Delayed-choice causal order and the reality of causal non-separability