We report strict verification of multiple types of indefinite causal orders and demonstrate distillation of indefinite causal order utilizing a programmable silicon-photonic quantum chip. This experimental implementation contributes to the development of a resource theory for indefinite causal order.
Indefinite causal order (ICO), a striking feature of quantum mechanics, has attracted broad theoretical and experimental interest. While ICO holds promise for quantum information processing, akin to quantum entanglement, its experimental realization and rigorous verification remain fundamental challenges. Here, we demonstrate and certify generalized multidimensional multipartite ICOs using a programmable integrated-photonic quantum chip implementing a generalized quantum switch. By violating definite causal order bounds with high statistical significance, we experimentally characterize and verify these generalized ICOs. Furthermore, we explore a resource theory of causal nonseparability by implementing a single-copy distillation protocol. Our Letter constitutes a major step toward a generalized framework for quantum causality.
A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite causal order provides a promising solution by allowing control over the sequence in which channels are applied. We experimentally demonstrate the activation of quantum communication through completely depolarizing channels using a programmable silicon photonic quantum chip. By implementing configurations based on the superposition of cyclic orders, a form of indefinite causal order, we report the first experimental realization of genuine quantum information transmission across multiple concatenated completely depolarizing channels. Our results show that when four completely depolarizing channels are combined using the superposition of cyclic orders, the fidelity of the output state is 0.712±0.013, significantly exceeding the classical threshold of 2/3. Our work establishes indefinite causal order as a powerful tool for overcoming noise-induced limitations in quantum communication, demonstrating its potential in high-noise environments and opening new possibilities for building robust quantum networks.
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.
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.
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.
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.