# Semi-device-independent certification of indefinite causal order

## TL;DR

This paper introduces a semi-device-independent framework to certify indefinite causal order in quantum processes, demonstrating that the quantum switch exhibits noncausal properties even when full device characterization isn't available.

## Contribution

It develops a new semi-device-independent certification method for noncausal quantum processes, expanding the understanding of quantum switch correlations beyond fully characterized scenarios.

## Key findings

- Quantum switch can exhibit noncausal properties semi-device-independently
- The framework certifies noncausality without full device characterization
- Quantum processes can show stronger noncausal correlations than previously known

## Abstract

When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario, where the involved operations are not characterised. Nevertheless, all physical implementations of process matrices proposed so far require full characterisation of the involved operations in order to certify such phenomena. Here we consider a semi-device-independent scenario, which does not require all operations to be characterised. We introduce a framework for certifying noncausal properties of process matrices in this intermediate regime and use it to analyse the quantum switch, a well-known higher-order operation, to show that, although it can only lead to causal statistics in a device-independent scenario, it can exhibit noncausal properties in semi-device-independent scenarios. This proves that the quantum switch generates stronger noncausal correlations than it was previously known.