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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Experimental tests of indefinite causal orders

Lee A. Rozema, Giulia Rubino, Adrien Feix, Mateus Araújo, Časlav Brukner, Philip John Walther

Published Jun 1, 2017• 0 citations
Publisher

Abstract

Summary form only given. A causal order describes the order in which events occur, and how these different events can effect each other. Recently, a description of quantum mechanics making no assumption about the order of events was developed [1]. In this formalism, events are treated in terms of the ability to exchange information between each other. Applying this new formalism to quantum mechanics has shown that processes without a defined causal order can exist. Information can nonetheless be transferred through these processes. Extraordinarily, these processes can accomplish tasks which are not otherwise possible [2-4]. In our group, we have been studying methods to create and characterize one such process: the “quantum SWITCH” [5, 6]. We have shown that, using this process, one can obtain computational advantages [5]. We have also performed a specific sequence of measurements, which we used to determine just how “non-causal” our constructed process is [6].

DOI
10.1109/cleoe-eqec.2017.8087315

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Summary form only given. A causal order describes the order in which events occur, and how these different events can effect each other. Recently, a description of quantum mechanics making no assumption about the order of events was developed [1]. In this formalism, events are treated in terms of the ability to exchange information between each other. Applying this new formalism to quantum mechanics has shown that processes without a defined causal order can exist. Information can nonetheless be transferred through these processes. Extraordinarily, these processes can accomplish tasks which are not otherwise possible [2-4]. In our group, we have been studying methods to create and characterize one such process: the “quantum SWITCH” [5, 6]. We have shown that, using this process, one can obtain computational advantages [5]. We have also performed a specific sequence of measurements, which we used to determine just how “non-causal” our constructed process is [6].
Investigating the role of causal order in quantum mechanics has recently revealed that the causal relations of events may not be a priori well defined in quantum theory. Although this has triggered a growing interest on the theoretical side, creating processes without a causal order is an experimental task. We report the first decisive demonstration of a process with an indefinite causal order. To do this, we quantify how incompatible our setup is with a definite causal order by measuring a "causal witness." This mathematical object incorporates a series of measurements that are designed to yield a certain outcome only if the process under examination is not consistent with any well-defined causal order. In our experiment, we perform a measurement in a superposition of causal orders-without destroying the coherence-to acquire information both inside and outside of a "causally nonordered process." Using this information, we experimentally determine a causal witness, demonstrating by almost 7 SDs that the experimentally implemented process does not have a definite causal order.
In recent years, operational approaches to quantum foundations have been developed as a means of understanding the core principles and distinctive features of quantum theory. Such approaches typically view physical processes as sequences of operations, with earlier operations serving as causes of later effects. However, a growing literature is emerging on the possibility of relaxing this assumption and allowing for quantum indefiniteness in the causal order. This development stems from a variety of motivations, both fundamental and applied, including exploring the role of causality in quantum theory, the interplay between quantum theory and general relativity, and higher-order quantum computing. A prominent offshoot of this development is the emergence of indefinite causal order as a feasible resource for quantum information processing. This review provides an overview of the current state of the art in the field, covering the methodology underlying indefinite quantum causality within the so-called "process matrix formalism", outlining key results and experimental implementations, and discussing recent advances.
Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is possible to formulate quantum mechanics without any reference to a global time or causal structure. The resulting framework includes new kinds of quantum resources that allow performing tasks—in particular, the violation of causal inequalities —which are impossible for events ordered according to a global causal order. However, no physical implementation of such resources is known. Here we show that a recently demonstrated resource for quantum computation—the quantum switch —is a genuine example of ‘indefinite causal order’. We do this by introducing a new tool—the causal witness —which can detect the causal nonseparability of any quantum resource that is incompatible with a definite causal order. We show however that the quantum switch does not violate any causal inequality.
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.
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.
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.