Quantum theory cannot violate a causal inequality

TL;DR

This paper demonstrates that, despite quantum superpositions of causal order, quantum experiments cannot violate causal inequalities, meaning classical causal models can simulate quantum results in this context.

Contribution

It proves that quantum theory cannot violate causal inequalities, contrasting with Bell inequalities, and shows classical models can replicate quantum causal superpositions.

Findings

Quantum superpositions of causal order exist in quantum theory.

Quantum experiments can be simulated by classical causal models.

Quantum theory cannot violate causal inequalities.

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.