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Quantum mechanics permits certain kinds of non-local effects. This paper demonstrates how these can be used for distributed computation with minimal communication between various processors. The problem considered is that of estimating the…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Analogies between quantum mechanics and sociology lead to the hypothesis that quantum objects are complex products of evolution. Like biological objects they are able to receive, to work on, and to spread semantic information. In general…
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…
Relational quantum mechanics (RQM) proposes an ontology of relations between physical systems, where any system can serve as an `observer' and any physical interaction between systems counts as a `measurement'. Quantities take unique values…
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism versus interpretation. In this note, we make a clear distinction between them and show that there…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
At the intersection of machine learning and quantum computing, Quantum Machine Learning (QML) has the potential of accelerating data analysis, especially for quantum data, with applications for quantum materials, biochemistry, and…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
A succinct statement and justification of all the principles necessary to understand and evaluate interpretations of quantum mechanics is given. These principles provide strong constraints on interpretations. They imply the particle-like…
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its…