Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs

TL;DR

This paper introduces a semi-device-independent method to certify causally nonseparable quantum processes using trusted quantum inputs, expanding the understanding of noncausal correlations beyond causal inequalities.

Contribution

It defines causally nonseparable distributed measurements and demonstrates certification of all bipartite causally nonseparable processes with trusted inputs.

Findings

Certain causally nonseparable processes generate noncausal correlations without violating causal inequalities.

All bipartite causally nonseparable process matrices can be certified with trusted quantum inputs.

Some processes can generate noncausal correlations even when they do not violate causal inequalities.

Abstract

While the standard formulation of quantum theory assumes a fixed background causal structure, one can relax this assumption within the so-called process matrix framework. Remarkably, some processes, termed causally nonseparable, are incompatible with a definite causal order. We explore a form of certification of causal nonseparability in a semi-device-independent scenario where the involved parties receive trusted quantum inputs, but whose operations are otherwise uncharacterised. Defining the notion of causally nonseparable distributed measurements, we show that certain causally nonseparable processes which cannot violate any causal inequality, including the canonical example of the quantum switch, can generate noncausal correlations in such a scenario. Moreover, by imposing some further natural structure to the untrusted operations, we show that all bipartite causally nonseparable process matrices can be certified with trusted quantum inputs.