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Towards a Device Independent Proof of Indefinite Causal Order with a Quantum Switch

Carla M. D. Richter, Michael Antesberger, Huan Cao, Philip John Walther, Lee A. Rozema

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Building on concepts from Bell inequalities, we experimentally realize a device-independent protocol proving that the quantum switch creates an indefinite causal order. This is achieved by entangling the switch’s control qubit with a ancilla photon.
DOI
10.1364/quantum.2025.qm3b.2

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Indefinite causal order can be realized by a quantum switch, yet its experimental certification has so far relied on assumptions about the devices. A device-independent verification of indefinite causal order would show, from the observed correlations alone and without relying on a detailed model of the devices, that they are incompatible with any classical description based on a fixed causal order. Here, we implement a photonic quantum switch in a device-independent scenario and test a Bell-like causal inequality using entangled photons. One photon serves as the control qubit of the quantum switch, while the other is measured by a distant party with rapidly and independently chosen settings. We observe a violation of the causal inequality by 24 standard deviations. These results provide experimental evidence for indefinite causal order, albeit in the presence of remaining loopholes, and mark an important step toward a fully loophole-free device-independent verification of causal indefiniteness in quantum processes.
Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations of indefinite causal order conditioned on assumptions on the devices used in the laboratory. But is a device-independent certification possible, similar to the certification of Bell nonlocality through the violation of Bell inequalities? Previous results have shown that the answer is negative if the switch is considered in isolation. Here, however, we present an inequality that can be used to device-independently certify indefinite causal order in the quantum switch in the presence of an additional spacelike-separated observer under an assumption asserting the impossibility of superluminal and retrocausal influences.
Quantum processes are transformations that act on quantum operations. Their study led to the discovery of the phenomenon of indefinite causal order: some quantum processes, such as the quantum switch, act on independent quantum operations in such a way that the order in which the operations are acted upon not only cannot be determined but is simply undefined. This is the property that we experimentally certify in this work. We report an experimental certification of indefinite causal order that relies only on the characterization of the operations of a single party. We do so in the semi-device-independent scenario with the fewest possible assumptions of characterization of the parties’ local operations in which indefinite causal order can be demonstrated with the quantum switch. To achieve this result, we introduce the concept of semi-device-independent causal inequalities and show that the correlations generated in a photonic quantum switch, in which all parties are able to collect local outcome statistics, achieve a violation of this inequality of 224 standard deviations. This result consists of the experimental demonstration of indefinite causal order with the fewest device-characterization assumptions to date.
Abstract Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations of indefinite causal order conditioned on assumptions on the devices used in the laboratory. But is a device-independent certification possible, similar to the certification of Bell nonlocality through the violation of Bell inequalities? Previous results have shown that the answer is negative if the switch is considered in isolation. Here, however, we present an inequality that can be used to device-independently certify indefinite causal order in the quantum switch in the presence of an additional spacelike-separated observer under an assumption asserting the impossibility of superluminal and retrocausal influences.
In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders—the so-called indefinite causal orders (ICOs)—which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of ICO have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of ICO would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of ICO in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of 1.8328 ± 0.0045 , which is 18 standard deviations above the definite causal order bound of 1.75 . Our work presents the first implementation of a device-independent protocol to verify ICO, albeit in the presence of experimental loopholes. This represents an important step toward the device-independent verification of an ICO and provides a context in which to identify loopholes specifically related to the verification of ICO.
Indefinite causal order has found numerous applications in quantum computation, quantum communication, and quantum metrology. Before its usage, the quality of the indefinite causal order needs to be first certified, and the certification should ideally be device independent (DI) to avoid the impact of device imperfections. In this work, we initiate the study of the sequential DI certification of an indefinite causal order. This can be useful in experimental platforms where the generation of an indefinite causal order is difficult. We show that an arbitrary number of sequential DI certifications of an indefinite causal order can be achieved with a quantum switch and also analyze practical requirements for experimental implementations of the certifications. Our work opens the possibility of reusing the resource of an indefinite causal order multiple times in device-independent quantum information processing.