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arXiv:1803.04302 · Physical Review Letters

Indefinite Causal Order in a Quantum Switch

Kaumudibikash Goswami, Christina Giarmatzi, Michael J. Kewming, Fabio Costa, Cyril Branciard, Jacquiline Romero, Andrew G. White

Published Aug 31, 2018• 245 citations
arXivHTMLPDF

Abstract

Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operations A[over ^] and B[over ^] act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound.

DOI
10.1103/physrevlett.121.090503

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Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operations A[over ^] and B[over ^] act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound.
The fundamental notion of fixed order between two events is challenged by formulations of quantum mechanics that makes no reference to a global time. The indefinite causal order arising from these formalisms can be realised using the quantum switch, a device where two operations can act in two different orders simultaneously. Similar to entanglement verification which employ entanglement witness, we verify indefinite causal order using a causal witness. In our experiment, we use polarisation as a control for the order of the operations that act on the spatial mode of a photon. We measure a causal witness value of -0.16±0.013, below the threshold of zero, thus demonstrating indefinite causal order in the quantum switch.
Classically, the causal order of two timelike separated events A and B is fixed-either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum switch is one of the most prominent processes with indefinite causal order. Optical realizations of the quantum switch have been successfully implemented in experiments, but some argue that this merely simulates a process with indefinite causal order and that a superposition of spacetime metrics is required for a true realization. Here, we provide a relativistic definition of causal order between operationally defined events that defines a meaningful observable in both the general relativistic and quantum mechanical sense. Importantly, this observable does not distinguish between the indefinite causal order implemented on an optical bench and the gravitational quantum switch, a gedanken experiment where the indefinite causal order is achieved by a quantum superposition of gravitational fields. Therefore, our results support the thesis that the optical quantum switch is just as much a realization of indefinite causal order as its gravitational counterpart, which makes use of the quantum mechanical behavior of spacetime.
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.
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.
Recent results have shown that quantum theory is compatible with novel causal structures where events happen without a definite causal order. In particular, the quantum switch describes a process in which two quantum channels act in a coherent superposition of their two possible orders. Furthermore, the quantum switch can perform communication tasks that are impossible within the framework of the standard quantum Shannon theory. The present paper considers the scenario of one-shot heralded qubit communication using a higher-order quantum switch constructed from two quantum switches. Specifically, we show that two quantum switches put in a superposition of their alternative causal orders can transmit a qubit, without any error, with a probability strictly higher than that achievable with each quantum switch. We discuss three examples that demonstrate this communication advantage. Notably, a higher-order quantum switch not only can outperform useful quantum switches but also becomes useful as a resource even if the quantum switches making it up are useless.
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.