Semi-device-independent certification of indefinite causal order

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.

17 + 22 pages. Code available at https://github.com/jessicabavaresco/SDI-causality. v5: Correction to the proof of Lemma 3. v6: Equation numbering amended in order to update the published version

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• Experimental superposition of time directions
• Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs
• Practical computational advantage from the quantum switch on a generalized family of promise problems
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• Network-Device-Independent Certification of Causal Nonseparability
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• "All-versus-nothing" proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario
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• Operational interpretation of the vacuum and process matrices for identical particles
• Sequential device-independent certification of indefinite causal order
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations
• No quantum advantage for violating fixed-order inequalities?