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The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
What belongs to quantum theory is no more than what is needed for its derivation. We argue for an approach focusing on reconstruction rather than interpretation of quantum mechanics and analyze several examples of reconstruction. We submit…
We investigate the class of physical theories with the same local structure as quantum theory, but a potentially different global structure. It has previously been shown that any bipartite correlations generated by such a theory must be…
The ontology emerging from quantum field theory and the results following from Bell's theorems allowed the development of an intuitive picture of the microscopic world described by quantum mechanics, that is, we can say that we understand…
One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably…
Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…