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We can recognize two modes in which 'quantum appears' in macro domains: (i) a 'micro-physical appearance', where quantum laws are assumed to be universal and they are transferred from the micro to the macro level if suitable 'quantum…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to…
This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…
Two theorems with applications to the quantum theory of measurements are stated and proven. The first one clarifies and amends von Neumann's Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one…
In a recent paper [quant-ph/9910066], Arens and Varadarajan gave a characterization of what they call EPR-states on a bipartite composite quantum system. By definition, such states imply perfect correlation between suitable pairs of…
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all…
Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show,…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown…
The production and manipulation of quantum correlation protocols will play a central role where the quantum nature of the correlation can be used as a resource to yield properties unachievable within a classical framework is a very active…
Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over…
A underlying dynamical structure for both relativity and quantum theory-``superrelativity'' has been proposed in order to overcome the well known incompatibility between these theories. The relationship between curvature of spacetime…
We assume that particles are point-like objects even when not observed. We report on the consequences of our assumption within the realm of quantum theory. An important consequence is the necessity of vacuum fields to account for particle…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
Physical systems in real life are inextricably linked to their surroundings and never completely separated from them. Truly closed systems do not exist. The phenomenon of decoherence, which is brought about by the interaction with the…
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess…