This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.
This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about using category theory in representing quantum computing and teleportation. We analyze very carefully the diagrammatic meaning of the usual representation of the Mach-Zehnder interferometer, and we show how it can be generalized to associate to each composition of unitary transformations a "laboratory quantum diagram" such that particles moving though the many alternate paths in this diagram will mimic the quantum process represented by the composition of unitary transformations. This is a finite dimensional way to think about the Feynman Path Integral. We call our representation result the Path Theorem. Then we go back to the basics of networks and matrices and show how elements of quantum measurement can be represented with network diagrams.
his book's main question-Is quantum mechanics non-local?-stilllooms large.But now we at least know that there can be no hope for a simple and unqualified "yes" or "no" answer to this riddle.There is such an enormous variety of interpretations of what constitutes a violation of the locality intuition, not to mention miscellaneous "degrees of severity" of these violations, that it would be utterly hopeless to expect a quick, onceand-for-all resolution to this problem.Yet we have made some progress.Along the quest to find the best counterfactual formulation of the condition of locality we have uncovered two possible interpretations of counterfactual conditionals which seem to be appropriate for describing quantummechanical phenomena that are in the center of our analysis.We should now take an important step forward and utilize these alternative interpretations to propose a precise formulation of the locality condition that could serve as a tenable explication for various intuitions associated with this notion.As we have already seen throughout this book, philosophers of physics and physicists alike often content themselves with pretty nebulous characterizations of the locality condition, of which the following are a representative sample:An event cannot be influenced by events in space-like separated regions.In particular, the outcome obtained in a measurement cannot be influenced by measurements performed in space-like separated regions; and analogously, possessed elements of physical reality referring to a system cannot be changed by actions taking place in space-like separated regions (Ghirardi & Grassi 1994).Since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system (Greenberger et al. 1990, p. 1132) For many purposes these descriptions may be considered sufficient, but without a thorough investigation into the possible meanings associated with terms such as "influence", "changed by", "in consequence of", etc. we T
Abstract Quantum Mechanics (QM) stands alone as a (very) successful physical theory, but the meaning of its variables and the status of many quantities in the mathematical formalism is obscure. This unique situation prompted the need for attribution of a physical meaning to the latter, a procedure known as interpretation. On the other hand, the study of QM is usually presented, even to future scientists, within the only framework developed by Bohr and the Copenhagen researchers, known as the Copenhagen interpretation. As a contribution to the understanding and teaching of Quantum Mechanics, aimed to a broader and deeper appreciation of its fundamentals, including contemplating alternatives and updated interpretations for physicists and philosophers interested in the study of exact sciences (through Ontology, Epistemology, Logic or the Theory of Knowledge), we present a set of Conceptual Diagrams elaborated and designed to expose and facilitate the visualization of elements intervening in any interpretation of Quantum Mechanics and apply them to several well‐developed cases of the latter.
This paper proposes an integrative ontological framework—termed the Self-Consistent Global Mode (SCGM) model—that addresses the conceptual gap between fundamental physics, quantum non-locality, and high-level emergent phenomenology. Drawing from relational quantum mechanics, integrated information theory, and the non-local real properties of the universe, we posit that the observable universe represents a single, self-consistent mathematical solution within a broader Hilbert space topology. Rather than treating fundamental physical laws as isolated mechanical constraints, the SCGM model formulates them as structural expressions of a fundamental, information-based "source code." Under this framework, dark matter, dark energy, and non-local quantum correlations are reinterpreted not as missing physical entities, but as boundary conditions, geometric tensions, or marginal projections between adjacent global modes of higher structural coherence. Furthermore, the paper explores how conscious observation and intentional systems might interact with these fundamental informational conduits. By framing physical reality as a hierarchical network of self-consistent modes, this model provides a non-dogmatic, logically structured foundation aimed at fostering future mathematical formalization and empirical testing regarding the nature of physical law and observer-system interactions.
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here, we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First, we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This 'it from bit' approach establishes an operational connection between local actions and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.