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.
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.
The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.
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].
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.
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.
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.
This work reports experimental evidence of indefinite causal order in a quantum process characterized by a 6×6 process matrix. The model was constructed step-by-step from an empirical basis of four distinct types of quantum experiments (Bell tests, Leggett-Garg inequalities, weak measurements, and delayed-choice experiments), naturally leading to an atypical quantum model that defies conventional interpretations. The emergent structure occupies an intermediate (Madhyamika) position between realism and QBism, exhibiting features that challenge both local and non-local descriptions in spatial and temporal domains. The model's characteristics align most closely with Carlo Rovelli's Relational Interpretation, where quantum properties are not absolute but exist in relation to specific physical interactions. Has similarities with TSVF and Costa de Beauregard's models, but also some significative differences. Using methods of causal projection and witness optimization, the study identifies signatures of causal indefiniteness, quantified by a causal error of 0.1488±0.0001. The process exhibits a 75% ICO score indicating moderate evidence of indefinite causal order, with CHSH value 2.753 achieving 90.95% of the standard quantum bound. The analysis includes comprehensive statistical validation via bootstrap methods and comparison with synthetic causal and non-causal processes. The causal incompatibility persists under bootstrap resampling with injected noise up to σ=0.01, demonstrating robustness of the effect. The experimental process shows 3.2× greater causal error than reference ICO benchmarks. So the model would be falsifiable through various types of experiments not difficult to design. Key quantum characteristics include entanglement negativity of 0.474 and total coherence of 0.315, supporting genuine quantum signatures beyond classical causal models. The complete Python code for the analysis, including process matrix optimization, causal projection, witness optimization, and statistical validation, is provided. The work not only contributes to understanding fundamental limits of quantum causality but also provides an empirically grounded framework that bridges multiple quantum phenomena within a unified relational context, potentially facilitating new approaches to quantum information processing beyond conventional causal structures.