Related papers: Quantum mechanics based on real numbers: A consist…
Quantum mechanics is very odd. It presents both an immensely practical and a deeply troubling conception of the physical world. As such, its uses stretch from optimizing nanoelectronics to examining the very nature of reality. In this…
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…
An attempt is made to formulate quantum mechanics (QM) in physical rather than in mathematical terms. It is argued that the appropriate conceptual framework for QM is "contextual objectivity", which includes an objective definition of the…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
The orthodox quantum mechanics can describe results of observation but not an objective reality. Misunderstanding of its positivistic essence results to numerous mistaken publications, in particular about a possibility of a real quantum…
Random numbers represent an indispensable resource for many applications. A recent remarkable result is the realization that non-locality in quantum mechanics can be used to certify genuine randomness through Bell's theorem, producing…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We use a simple example to illustrate why it is not possible to consider that a measurement reveals an underlying objective reality of a property of a quantum system, that continues the same after the measurement is performed. This kind of…
From the very beginning, Quantum Mechanics has been accompanied by crucial foundational questions: the possibility of visualizing physical processes, the limits of measurement epitomized by the Heisenberg uncertainty principle, the…
We use quantum computers to test the foundations of quantum mechanics through quantum algorithms that implement some of the experimental tests as the basis of the theory's postulates. These algorithms can be used as a test of the physical…
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more…
Various fundamental phenomena of strongly-correlated quantum systems such as high-$T_c$ superconductivity, the fractional quantum-Hall effect, and quark confinement are still awaiting a universally accepted explanation. The main obstacle is…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…