Quantum information technology is one of the fastest growing sectors within information technology. This paper is a conjecture about expected boundary conditions of nonlocal effects and shows the consequences of definite or indefinite causal order of entangled quantum events leading to causality. It focuses on nonlocal causality in relativistic systems, and introduces the notion of quantum causal coherence as a nonlocal property of relativistic causality, reflecting the relation of entanglement and the principle of least action. It is shown, that the principle of least action is the self-consistency mechanism of nonlocal causality in relativistic scenarios, especially in timelike scenarios of entangled quanta. From the view of relativistic scenarios, this paper examines the possibility of causal loops in quantum causal relations and investigates quantum causal relations in well established experiments.
Quantum information technology is one of the fastest growing sectors within information technology. This paper is a conjecture about expected boundary conditions of nonlocal effects and shows the consequences of definite or indefinite causal order of entangled quantum events leading to causality. It focuses on nonlocal causality in relativistic systems, and introduces the notion of quantum causal coherence as a nonlocal property of relativistic causality, reflecting the relation of entanglement and the principle of least action. It is shown, that the principle of least action is the self-consistency mechanism of nonlocal causality in relativistic scenarios, especially in timelike scenarios of entangled quanta. From the view of relativistic scenarios, this paper examines the possibility of causal loops in quantum causal relations and investigates quantum causal relations in well established experiments.
Quantum information technology is one of the fastest crowing sectors within information technology. This paper is a conjecture about expected boundary conditions of nonlocal effects and shows the consequences of definite or indefinite causal order of entangled quantum events leading to causality. It focuses on nonlocal causality in relativistic systems, and introduces the notion of quantum causal coherence as a nonlocal property of relativistic causality, reflecting the relation of entanglement and the principle of least action. It is shown, that the principle of least action is the self-consistency mechanism of nonlocal causality in relativistic scenarios, especially in timelike scenarios of entangled quanta. From the view of relativistic scenarios, this paper examines the possibility of causal loops in quantum causal relations and investigates quantum causal relations in well established experiments.
Quantum information technology is one of the fastest growing sectors within information technology. By misleading interpretations of Bohr's definition of complementarity, the foundation of nonlocal correlations of entanglement is concealed and therefore, such nonlocal effects can apparently not be utilized directly in information technology. As the first step to identify the utilizable nonlocal property of entanglement, this paper adjusts the notion of complementarity of first-order and second-order interference. Especially, the nonlocal consequence of the "principle of least action" for entangled systems is shown by the foundation of second-order interference, the shared phase solutions space. Based on the concept of Feynman's path integral, the validity of the theory is demonstrated by applying the theory to well-known experiments, revealing this underlying nonlocal principle. In the next steps of publication, to highlight the relevance of this nonlocal principle for quantum computing and quantum information technology, the "self-consistency principle" of such nonlocal quantum causal correlations will be shown and verified by an experiment.
Recent frameworks describing quantum mechanics in the absence of a global causal order admit the existence of causally indefinite processes, where it is impossible to ascribe causal order for events A and B. These frameworks even allow for processes that violate so-called causal inequalities, which are analogous to Bell's inequalities.However, the physicality of these exotic processes is, in the general case, still under debate, bringing into question their foundational relevance.While it is known that causally indefinite processes can be probabilistically realized by means of a quantum circuit, along with an additional conditioning event C, concrete insights into the ontological meaning of such implementation schemes have heretofore been limited.Here, we show that causally indefinite processes can be realized with schemes where C serves only as a classical flag heralding which causally indefinite process was realized.We then show that there are processes where any pure conditioning measurement of C leads to a causally indefinite process for A and B, thus establishing causal indefiniteness as a basis-independent quantity.Finally, we demonstrate that quantum mechanics allows for phenomena where C can deterministically decide whether A comes before B or vice versa, without signaling to either.This is akin to Wheeler's famous delayedchoice experiment establishing definite causal order in quantum mechanics as an instrument-dependent property.
In recent years, the investigation of causal relations in quantum theory has attracted a lot of interest. In particular, it has been found that it is possible to conceive of scenarios where some parties perform operations that are compatible with quantum theory locally, but that cannot be embedded into a global background causal structure. Such indefinite causal structures are of interest from a fundamental point of view, but also from the perspective of quantum information processing, since they do not fit into the usual paradigm of quantum circuits, which assumes a definite causal order. The main aim of this thesis is to study indefinite quantum causal relations involving more than two parties. Compared to the bipartite case, there are many new aspects and complications that arise in multipartite situations, which need to be clarified in order to fundamentally understand quantum causal structures, and to shed light on their implications and potential usefulness for quantum information processing.A suitable mathematical framework for the investigation of quantum causal relations is the process matrix formalism. In this framework, the notion of causal nonseparability was introduced in order to qualify scenarios that are incompatible with a definite causal order. In Chapter 2, we study how to generalise this concept to the multipartite case, how to characterise multipartite causally (non)separable quantum processes, and how to certify multipartite causal nonseparability. Another important topic is to determine which quantum scenarios with indefinite causal order are physically implementable, and how they can be realised concretely. In Chapter 3, we introduce two new classes of physically realisable multipartite quantum processes, and characterise them in terms of their process matrix descriptions. In particular, we define the class of quantum circuits with quantum control of causal order. The simplest example of such a circuit is the quantum switch, a protocol in which the order between two operations is controlled by a qubit in a superposition state, and which defines a causally nonseparable process. The class we introduce also contains more general examples of causally nonseparable processes with new features. We then show how the process matrix characterisation of this class allows us to search for new quantum information processing applications of causal nonseparability. In Chapter 4, we investigate a particular quantum communication effect in a scenario involving coherent control between two quantum channels. This leads us to a more general analysis of the notion of a coherently controlled channel, which involves certain subtilities. In Chapter 5, we turn to another problem that arises in multipartite scenarios, namely whether a given phenomenon is genuinely multipartite or not. More particularly, we study genuinely multipartite (non)causal correlations. In Chapter 6, we show that anomalous weak values are possible without post-selection. In Chapter 7, we show that certain tripartite process matrices, namely those that are unitarily extensible, have a realisation on so-called time-delocalised subsystems, i.e., quantum subsystems that are not associated with a definite time. The class of unitarily extensible tripartite process matrices is larger than the class of quantum circuits with quantum control, and in particular contains processes that violate so-called causal inequalities.
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.
Abstract We advance the Information Boundary Principle (IBP): an event becomes irreversible when its informational content is recorded or irreversibly entangled with the environment, thereby fixing it within globally consistent boundary conditions across spacetime. In delayed‑choice quantum eraser experiments, correlations appear to allow future measurements to determine past behavior. We argue these results reveal a boundary‑value structure of quantum reality: histories are selected to satisfy both initial and final constraints, with inconsistency forbidden by the information boundary. We formalize the IBP using density‑matrix dynamics, decoherence, mutual information, and the Englert duality relation, derive observational consequences for eraser‑type experiments, and outline empirical tests capable of discriminating our view from competing interpretations. While fully consistent with special and general relativity, the IBP imposes an additional global constraint on their solution space. Einstein’s equations admit mathematically valid but unphysical spacetimes—tachyonic world‑lines, closed timelike curves, traversable wormholes sustained by exotic matter, and naked singularities. As energy conditions, quantum stability, and Hawking’s chronology‑protection principle already restrict many such solutions, the IBP further filters the admissible set by excluding any geometry that cannot maintain coherent, non‑contradictory informational records. Thus the IBP acts as an information‑theoretic selection rule layered over, not against, relativity’s geometry. Keywords: delayed choice; quantum eraser; decoherence; mutual information; causality; two‑state vector; information theory; relativity.