Quantum Switch and Teleportation.

This work develops a process-based interpretation of quantum teleportation, quantum switching, and time, grounded in discrete process graphs rather than continuous space–time dynamics. We introduce a formal framework in which the fundamental unit of physical evolution is not the quantum state itself, but a discrete process step (process tact), represented as a unitary transformation acting on a structured process graph. Quantum teleportation is reinterpreted as a transition between isomorphic index layers of the same process graph, rather than as a transmission of a quantum state through space–time. In this framework, entanglement establishes a shared structural constraint, measurement performs index selection, and classical communication transfers index information only. The quantum state remains invariant under graph isomorphism, and teleportation is formalized as reindexation without a physical carrier. Time is shown to emerge as an ordering relation between process steps and index layers, not as a fundamental parameter. Changes in temporal ordering correspond to transitions between equivalent graph embeddings, enabling a natural interpretation of temporal displacement as index reassignment within a recursive process structure. Geometrically, these ideas are represented using recursive pentagon–pentagram embeddings, which serve as an exact structural analogy for quantum switching. The pentagram functions as a universal quantum switch, mediating transitions between distinct but isomorphic orderings. This construction provides an intuitive and mathematically consistent representation of indefinite causal order. The framework is directly connected to EPR correlations, quantum teleportation protocols, and the quantum switch, and is shown to be naturally compatible with the Everett (many-worlds) interpretation of quantum mechanics. Within this ontology, the wave function is treated as an objective process structure, and no collapse postulate is required. This work builds upon and extends previously published results on graph-based quantum key switching and emergent space–time structure, unifying them into a single process-theoretic description of quantum information transfer, causal order, and temporal indexing. Reference to previous foundational work: DOI 10.5281/zenodo.18498181. Reference to previous foundational work: DOI 10.5281/zenodo.18504244.