Network-Device-Independent Certification of Causal Nonseparability

TL;DR

This paper introduces a method to certify the causal nonseparability of quantum processes, including the quantum switch, in a device-independent manner using observed correlations and untrusted operations.

Contribution

It provides the first device-independent certification method for causal nonseparability of processes with trusted quantum inputs, including the quantum switch.

Findings

Certifies causal nonseparability in a device-independent way

Includes certification of the quantum switch

Uses a network of untrusted operations for self-testing

Abstract

Causal nonseparability is the property underlying quantum processes incompatible with a definite causal order. So far it has remained a central open question as to whether any process with a clear physical realisation can violate a causal inequality, so that its causal nonseparability can be certified in a device-independent way, as originally conceived. Here we present a method solely based on the observed correlations, which certifies the causal nonseparability of all the processes that can induce a causally nonseparable distributed measurement in a scenario with trusted quantum input states, as defined in [Dourdent et al., Phys. Rev. Lett. 129, 090402 (2022)]. This notably includes the celebrated quantum switch. This device-independent certification is achieved by introducing a network of untrusted operations, allowing one to self-test the quantum inputs on which the effective distributed measurement induced by the process is performed.