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

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.

6 + 17 pages, 1 figure. v2: updated to published version

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• Quantum Circuits Architecture
• Experimental Verification of an Indefinite Causal Order
• Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
• Quantum circuits with classical versus quantum control of causal order
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Cited by in corpus (7)

• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Semi-device-independent certification of indefinite causal order in a photonic quantum switch
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Network-Device-Independent Certification of Causal Nonseparability
• Emergent non-Markovianity and dynamical quantification of the quantum switch
• Sequential device-independent certification of indefinite causal order
• No quantum advantage for violating fixed-order inequalities?