Atemporal diagrams for quantum circuits (17 pages)

Ville Bergholm, Juha J. Vartiainen

Colin P. Williams, Farrokh Vatan

Robert B. Griffiths, Shengjun Wu, Li Zhi Yu +1 more

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.

Ayan Datta, P Prabhavathi

David Rieck

The foundational framework herein termed APSF has been substantially revised and restated as the Atemporal Substrate Ontology (ASO) [link], which supersedes it in name, scope, and evidential framing. ABES (Atemporal Boundary Encoded Substrate) proposes a reframing of quantum foundations and quantum-gravitational unification. It synthesizes the Wheeler-DeWitt equation and holographic boundary encoding to identify an atemporal, pre-spatial information substrate — static correlations that reinterpret what the wave function describes, without altering its mathematics. This paper is one application of the Atemporal Substrate Ontology (ASO) incorporating Holographic Principle.The framework rests on two principles: (1) systems unable to support 3+1D spacetime architecture must confine information to boundary encodings, and (2) atemporality is the default for such states. Both are independently supported by established physics. A host of quantum enigmas — from the measurement problem to non-locality to the arrow of time — dissolve as artifacts of the transition from atemporal substrate to bound spacetime.ABES is agnostic on emergent versus fundamental time, compatible with Page-Wootters, Zurek decoherence, and Copenhagen interpretations alike. It introduces no new equations, particles, or dimensions — only a reinterpretation of what existing mathematics describes. The paper includes formal derivations from explicit premises (Appendix C), a path toward mathematical formalization (Appendix A), and verified computational demonstrations (Appendix B).The framework complements rather than competes with leading programs. An atemporal 1D string, for instance, offers string theory a path forward without altering its existing machinery. Similar clean integrations apply to loop quantum gravity, emergent gravity, and quantum information theory.This is a comprehensive paper covering quantum foundations, eleven physics enigmas, quantum-gravitational unification, and testable distinguishing predictions.

Jack D. Hidary