Related papers: Quantum Covariance and Filtering
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics,…
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…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…
Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.
Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are…
Deeper insight leads to better practice. We show how the study of the foundations of quantum mechanics has led to new pictures of open systems and to a method of computation which is practical and can be used where others cannot. We…
The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the introduction of axiomatic observables. The conventional (collapse) and the Everett interpretations of…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
Weaver has recently defined the notion of a quantum relation on a von Neumann algebra. We demonstrate that the corresponding notion of a quantum function between two von Neumann algebras coincides with that of a normal unital…
Within the framework of the algebraic approach the problem of hidden parameters in quantum mechanics is surveyed. It is shown that the algebraic formulation of quantum mechanics permits introduction of a specific hidden parameter, which has…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
Quantum theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…