Description / Abstract:This research explores the emergence of indefinite causal order within quantum systems through the lens of the Quantum Switch and Everettian quantum mechanics. By formalizing the concept of discrete P-tacts—primitive process units composed of local unitaries and entangling operations—the work introduces flat acts as fundamental structures representing coherent process sequences. The study develops a graphical framework of P-tact networks to represent superpositions of causal orders, demonstrating how indefinite causal relations can be realized without invoking wavefunction collapse. Experimental implications include connections to EPR experiments, quantum teleportation, and Mach–Zehnder interferometry. This approach provides a novel, process-oriented formalism unifying quantum causality, entanglement, and Everettian branching, suitable for applications in quantum information processing and foundational physics.
Description / Abstract:This research explores the emergence of indefinite causal order within quantum systems through the lens of the Quantum Switch and Everettian quantum mechanics. By formalizing the concept of discrete P-tacts—primitive process units composed of local unitaries and entangling operations—the work introduces flat acts as fundamental structures representing coherent process sequences. The study develops a graphical framework of P-tact networks to represent superpositions of causal orders, demonstrating how indefinite causal relations can be realized without invoking wavefunction collapse. Experimental implications include connections to EPR experiments, quantum teleportation, and Mach–Zehnder interferometry. This approach provides a novel, process-oriented formalism unifying quantum causality, entanglement, and Everettian branching, suitable for applications in quantum information processing and foundational physics.
This work develops a graph-theoretic and process-based foundation for indefinite causal order in quantum theory, demonstrating that causal indefiniteness is not an ad hoc or exotic phenomenon but an emergent structural property of quantum dynamics when the primitive unit of evolution is taken to be the П-такт (P-Tact) — a discrete quantum process composed of local unitary superposition and entangling unitary interaction. Building upon a sequence of previously published foundational works, this paper formulates indefinite causal order as a superposition of quantum process graphs, where each graph encodes a definite causal structure, and the quantum state corresponds to a coherent superposition over such graphs. Within this framework, causal order is not fundamental but arises only in coarse-grained or classical limits. We show that: Indefinite causal order naturally emerges from the superposition of process graphs, without invoking external control systems or higher-order operations. The quantum switch is reinterpreted as a special finite realization of a more general graph-superposition principle. Time and causality emerge as effective parameters in the infinite-graph (continuum) limit of discrete П-такт dynamics. The graph-theoretic formulation is fully compatible with — and structurally supports — the Everettian (Many-Worlds) interpretation, where branching corresponds to graph bifurcations rather than wavefunction collapse. Classical spacetime causality appears as a macroscopic ordering imposed on an underlying non-causal quantum substrate. This approach unifies quantum information, indefinite causal order, emergent temporality, and Everettian branching within a single formal framework based on discrete process units and their graph composition. The results close several open conceptual gaps in the interpretation of quantum switches, process matrices, and non-classical causal structures, offering a consistent ontology grounded in quantum dynamics itself. This paper directly builds upon and extends the following foundational works: Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт). Zenodo.https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Quantum Switch and Teleportation. Zenodo.https://doi.org/10.5281/zenodo.18509173 Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics. Zenodo.https://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). P-Tact (П-такт) as the Primitive Unit of Quantum Theory. Zenodo.https://doi.org/10.5281/zenodo.18516711 Together, these works establish a coherent program aimed at demonstrating the universality of quantum mechanics, the absence of fundamental collapse, and the emergence of spacetime and causality from discrete quantum process dynamics.
This work introduces the П-Tact (P-Tact) as the primitive unit of quantum theory, providing a formal, mathematical, and experimentally grounded framework for describing quantum processes at both micro and macro scales. A П-Tact represents a discrete process unit, consisting of two combined unitary operations: a local unitary operation that creates superposition and an entangling unitary operation that establishes quantum connections between nodes. The theory rigorously defines how quantum information propagates through graphs of П-Tacts, giving rise to emergent structures, including space, time, and causal order. We demonstrate how this framework unifies multiple aspects of quantum mechanics: indefinite causal order, quantum switch dynamics, quantum teleportation, and Everettian branching of quantum states. The formalism is expressed through precise unitary operations, mathematical derivations, and illustrative diagrams of П-Tact networks, quantum switch cycles, and emergent Everettian subgraphs. By introducing the П-Tact as the fundamental unit, this work offers a new methodology for understanding the discrete structure of quantum processes and provides a bridge between quantum foundations, quantum information theory, and emergent space-time concepts. Key contributions include: Formal definition and mathematical characterization of П-Tact (P-Tact) as the primitive unit of quantum processes. Construction of quantum network graphs representing information flow and entanglement between П-Tacts. Demonstration of indefinite causal order and quantum switch dynamics at both micro- and macro-levels. Illustration of emergent branching structures corresponding to Everettian subgraphs and classical outcomes. Establishment of a discrete framework connecting quantum dynamics with emergent space-time and topological structures. This publication is suitable for researchers in quantum information, quantum computing, quantum communication, quantum foundations, and theoretical physics, providing both theoretical insights and experimental guidance for exploring discrete quantum process units and their applications in emerging quantum technologies. 1. Pavlov, M. (2026 ). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт)https://doi.org/10.5281/zenodo.18498181 2. Pavlov, M. (2026 ). Quantum Switch and Teleportationhttps://doi.org/10.5281/zenodo.18509173 3. Pavlov, M. (2026 ). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamicshttps://doi.org/10.5281/zenodo.18504244
Description This work develops a process-based reconstruction of the quantum switch and the notion of indefinite causal order by introducing P-tacts (П-tacts) as the primitive units of quantum dynamics. Within this framework, quantum evolution is not described as a sequence of time-ordered operations but as a composition of discrete process units connected through explicit topological relations. The present article builds directly on the foundational introduction of the P-tact as the primitive unit of quantum theory, where process is taken as ontologically prior to state and time is not assumed as a fundamental parameter(Pavlov, P-Tact (П-такт) as the Primitive Unit of Quantum Theory, Zenodo, 2026, DOI: 10.5281/zenodo.18516711). In earlier work, this process ontology was applied to the quantum switch, demonstrating that its behavior emerges naturally from discrete process connectivity rather than from fundamentally indefinite causal relations(Pavlov, Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт), Zenodo, 2026, DOI: 10.5281/zenodo.18498181). The connection between quantum switch behavior and quantum teleportation was subsequently clarified, showing that teleportation can be interpreted as a reindexing of process relations within a shared process topology(Pavlov, Quantum Switch and Teleportation, Zenodo, 2026, DOI: 10.5281/zenodo.18509173). Furthermore, the same P-tact framework was shown to give rise to emergent causality, time, gravity, and three-dimensional space as derived properties of discrete process graph dynamics rather than as fundamental background structures(Pavlov, Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact Dynamics, Zenodo, 2026, DOI: 10.5281/zenodo.18504244). In the present work, these results are unified and extended through the explicit introduction of superposition of process graphs as a formal object. Using pentagonal and pentagram (pentacle) structures constructed from P-tacts, the quantum switch is reconstructed as a definite process topology. The appearance of indefinite causal order is shown to arise solely from projecting this topology onto a time-indexed formalism. No global temporal parameter is required at the fundamental level. All process relations are explicitly defined through connectivity, and control operations occupy superpositions of topological positions, not temporal slots. As a result, indefinite causal order is reclassified as a methodological placeholder, signaling the breakdown of time-based descriptive language rather than a fundamental indeterminacy of nature. The framework preserves all experimentally verified predictions while restoring conceptual coherence. It aligns naturally with the Everett interpretation of quantum mechanics, maintaining universal unitarity and eliminating collapse or exceptional measurement postulates. Quantum branching is interpreted as divergence in process graphs rather than as stochastic temporal events. This work prepares the conceptual and formal ground for subsequent studies on process-based quantum computation and programming, where local, dynamically entangled process modules replace long, phase-accumulating quantum circuits, offering a new architectural approach to decoherence and scalability.
The Everett interpretation of quantum mechanics establishes a radical but internally consistent premise: the universal wave function evolves unitarily and deterministically at all times, without collapse and without any privileged notion of measurement. While this framework has been extensively discussed at the conceptual level, many of its structural implications—particularly concerning causality, temporal order, and process composition—have remained only implicitly formulated. In this work, we present a systematic formalization of Everett’s process logic using discrete process units (P-Tacts) and show that the quantum switch naturally emerges as a minimal closed P-Tact cycle. Within this framework, indefinite causal order is not introduced as an additional postulate or informational resource, but arises as a direct consequence of cyclic unitary process composition, fully consistent with universal quantum evolution. We begin by revisiting Everett’s relative-state formulation from a process-theoretic perspective. Everett’s insistence on the universality of unitary dynamics already removes any fundamental distinction between “before” and “after” at the level of the global wave function. However, without an explicit discrete process structure, the emergence of causal relations and effective temporal ordering remains conceptually underdetermined. The P-Tact framework addresses this gap by identifying the primitive unit of quantum dynamics as a discrete, operationally realizable unitary process step, rather than a continuous time parameter. By constructing closed cycles of P-Tacts, we demonstrate that causal relations become relational properties of process graphs rather than reflections of an underlying time axis. The minimal non-trivial realization of such a cycle corresponds precisely to the operational structure of the quantum switch. In this setting, the control system does not select between alternative temporal orders; instead, it coherently selects between alternative process paths within a closed P-Tact cycle. Indefinite causal order thus appears as an intrinsic structural feature of the process graph, not as a violation or suspension of causality. This interpretation places the quantum switch firmly within the Everettian framework. Rather than extending or modifying Everett’s interpretation, the quantum switch operationally realizes one of its latent consequences: the coexistence and coherent superposition of multiple process orderings within a single universal wave function. The absence of a fundamental time parameter in Everett’s theory finds a concrete expression here, where effective temporal order emerges only upon projection of the underlying cyclic process structure onto an acyclic subgraph. Furthermore, the P-Tact cycle formalism provides a unifying language connecting several previously distinct domains: quantum control of causal order, quantum teleportation, entanglement-mediated process composition, and the emergence of time and causality from unitary dynamics. From this perspective, the quantum switch represents not an isolated protocol, but the simplest experimentally accessible manifestation of a general class of Everettian process cycles. In conclusion, this work advances Everett’s original program by making explicit the process-level structures implicit in his formulation. The quantum switch, understood as a minimal P-Tact cycle, serves as a concrete bridge between foundational quantum theory and modern experiments on indefinite causal order. In doing so, it demonstrates that recent developments in quantum information theory do not depart from Everett’s vision, but instead bring it to a new level of formal and operational clarity. Bibliography Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт).Zenodo. https://doi.org/10.5281/zenodo.18498181 Quantum Switch and Teleportation.Zenodo. https://doi.org/10.5281/zenodo.18509173 Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics.Zenodo. https://doi.org/10.5281/zenodo.18504244 P-Tact (П-такт) as the Primitive Unit of Quantum Theory.Zenodo. https://doi.org/10.5281/zenodo.18516711 Indefinite Causal Order as Superposition of Process Graphs.Zenodo. https://doi.org/10.5281/zenodo.18519010 Everett Interpretation Formalized via P-Tact (П-такт) Path Graphs.Zenodo. https://doi.org/10.5281/zenodo.18524745 Emergence of Time from P-Tact Entanglement (Происхождение времени).Zenodo. https://doi.org/10.5281/zenodo.18526015 From Indefinite Causal Order to Definite Process Order:A Topological Reconstruction of the Quantum Switch via Discrete P-Tacts (П-такт).Zenodo. https://doi.org/10.5281/zenodo.18526959 Causality and Arrow of Time.Zenodo. https://doi.org/10.5281/zenodo.18549931
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.
Description This work presents a process-based quantum framework in which causality, gravity, time, and three-dimensional space emerge from discrete quantum processes (P-tacts). A P-tact is defined as a minimal unit of quantum evolution combining a local superposition operation and an entangling unitary transformation. The global dynamics of a system is described as a graph of P-tacts, where causal order, branching, and relational structure arise intrinsically, without introducing an external time parameter. The framework demonstrates that causal branching appears first, followed by emergent quantum gravity as an effect of entanglement density and network connectivity. From this structure, relational time emerges as a discrete sequence of P-tacts, and only at later stages does three-dimensional space arise from the global topology of the process graph. Space, time, and gravity are thus shown to be mutually emergent properties of a single discrete quantum process network. This work directly builds upon the previously published concept of the quantum switch as an emergent process structure from discrete P-tacts (see Ref. [1]) and extends it toward a unified description of spacetime emergence. The formalism provides a concrete realization of Everettian branching, making the many-worlds interpretation operational and graph-theoretic. The proposed framework connects quantum information theory, indefinite causal order, quantum gravity, and emergent spacetime, offering both conceptual clarity and experimental relevance. It is applicable to quantum switches, multi-qubit entanglement, quantum networks, and quantum simulations, and provides a testable route toward understanding spacetime as a derived structure rather than a fundamental background. Reference to previous foundational work: DOI 10.5281/zenodo.18498181.