Related papers: Embedding Quantum Universes into Classical Ones
Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle,…
In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be…
The spectacular successes of quantum physics have made it a commonplace to assert that we live in a quantum world. This idea seems to imply a kind of "quantum fundamentalism" according to which everything in the universe (if not the…
It is argued that the orthodox interpretation of quantum mechanics is in conflict with the objective existence of space-time, and suggested that kets are labels which name real states of matter but do not directly describe them. Position is…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is…
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.…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory…