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Photonics for Quantum (PfQ)

Quantum processes without a causal order

Lee A. Rozema, Michael Antesberger, Philip John Walther

Published Jul 19, 2022• 0 citations
Publisher

Abstract

Less than ten years ago it was realized that quantum theory permits the existence of processes which do not have a defined causal order. To date, several experiments have confirmed the existence of one such process, called the quantum SWITCH, in which it is impossible to say which of two parties acts first. This has since spawned a new field of research on quantum processes with an indefinite causal order. Building on a mathematical analogy to entanglement certification, various methods to quantify the lack of a causal order have been proposed and demonstrated. These characterization techniques range from playing specially designed games to the measurement of a so-called causal witness. Despite these promising strategies, there has not yet been a complete characterization of the quantum SWITCH and no measurement of its process fidelity. Here we present a new protocol to perform causal tomography which we carry out using a novel implementation of the quantum SWITCH, based on time-bin qubits in optical fiber. Our new implementation is readily scalable to more than two parties and, hence, could be used to observe the scaling advantages of certain quantum games. Using this platform, we perform the first measurement of the process fidelity of the quantum SWITCH.

DOI
10.1117/12.2634271

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Less than ten years ago it was realized that quantum theory permits the existence of processes which do not have a defined causal order. To date, several experiments have confirmed the existence of one such process, called the quantum SWITCH, in which it is impossible to say which of two parties acts first. This has since spawned a new field of research on quantum processes with an indefinite causal order. Building on a mathematical analogy to entanglement certification, various methods to quantify the lack of a causal order have been proposed and demonstrated. These characterization techniques range from playing specially designed games to the measurement of a so-called causal witness. Despite these promising strategies, there has not yet been a complete characterization of the quantum SWITCH and no measurement of its process fidelity. Here we present a new protocol to perform causal tomography which we carry out using a novel implementation of the quantum SWITCH, based on time-bin qubits in optical fiber. Our new implementation is readily scalable to more than two parties and, hence, could be used to observe the scaling advantages of certain quantum games. Using this platform, we perform the first measurement of the process fidelity of the quantum SWITCH.
The field of indefinite causal order (ICO) has seen a recent surge in interest. Much of this research has focused on the quantum switch, wherein multiple parties act in a superposition of different orders in a manner transcending the quantum circuit model. This results in a new resource for quantum protocols, and is exciting for its relation to issues in foundational physics. The quantum switch is also an example of a higher-order quantum operation, in that it transforms not only quantum states but also other quantum operations. To date, no quantum process without a definite causal order has been completely experimentally characterized. Indeed, past work on the quantum switch has confirmed its ICO by measuring causal witnesses or demonstrating resource advantages, but the complete process matrix has been described only theoretically. Here we report our performing higher-order quantum process tomography. However, doing so requires exponentially many measurements with a scaling worse than that of standard process tomography. We overcome this challenge by creating a new fiber-based quantum switch using active optical elements to deterministically generate and manipulate time-bin encoded qubits. Moreover, our new architecture for the quantum switch can be readily scaled to multiple parties. By reconstructing the process matrix, we estimate its fidelity and tailor different causal witnesses directly for our experiment. To achieve this, we measure a set of tomographically complete settings, which also spans the input operation space. Our tomography protocol allows the characterization and debugging of higher-order quantum operations with and without an ICO, while our experimental time-bin techniques could enable the creation of a new realm of higher-order quantum operations with an ICO. Published by the American Physical Society 2024
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.
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 with indefinite causal order challenge the classical assumption that operations must occur in a single fixed temporal sequence. The quantum switch provides a concrete setting in which two operation orders, A≺B and B≺A, are coherently controlled by a quantum system. In the strict process matrix formulation of the lazy guess your neighbour’s input (LGYNI) game, however, quantum theory, including the quantum switch, does not violate the standard causal inequality when probabilities are computed solely from local instruments. In this work, we study an extended control-assisted operational protocol in which the control system of the quantum switch is measured and used to define the task output. We compare increasingly expressive strategy classes, including single-qubit SU(2) operations, product target-ancilla operations, and entangling Cartan-decomposed two-qubit operations with generalized POVMs. Restricted models saturate or remain below the 3/4 fixed-order benchmark, whereas the optimized Cartan + ancilla + POVM strategy reaches Psuccext≈0.83596, demonstrating enhanced task performance within the extended protocol. The optimized strategy remains operationally no-signaling to numerical precision and retains its extended protocol advantage under more than 25% white noise admixture. These results identify the operational resources required for control-assisted quantum switch enhancement and support the view that indefinite temporal order can be used as a quantum informational resource without implying a breakdown of operational causality.
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.
Processes with indefinite causal order (ICO), such as the quantum switch, are an emerging resource for quantum tasks and a fundamental test bed for studies of temporal correlations in quantum mechanics. A limitation of past photonic implementations of the quantum switch, however, is their inability to perform measurements inside the switch without either destroying the superposition of causal orders or delaying readout until the after the quantum switch. Measurements where the results are read out locally are needed for several applications of ICO, but also for a loophole-free verification of ICO. Here, we overcome past limitations by introducing a local\mathit{local}local measurement scheme and coupling the photon in the switch to a time−delocalized\mathit{time-delocalized}time−delocalized ancilla system. We experimentally realize this protocol using a photonic quantum switch with post-selected linear optical logic gates. Our method ensures that the measurement apparatus interacts with the system at two distinct times and yet yields a single outcome. We use a quantum eraser measurement to preserve the ICO, which we certify by measuring a causal witness and finding a negative value of CW≈−0.305(1)\mathcal{C}_W \approx -0.305 (1)CW​≈−0.305(1). Furthermore, by explicitly realizing a time-delocalized ancilla system, our protocol not only enables a new class of quantum switch protocols requiring local readout, but also provides a general method for path-coherence-preserving measurements with broad applications beyond ICO.