Related papers: Some conceptual issues involving probability in qu…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
Under broad conditions, we prove that the probability amplitudes in the quantum mechanics are either always constant in time or changing continuously in any interval of time.
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Certain concrete "ontological models" for quantum mechanics (models in which measurement outcomes are deterministic and quantum states are equivalent to classical probability distributions over some space of `hidden variables') are…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
We discuss reasons why a probability amplitude, which becomes a probability density after squaring, is considered as one of the most basic ingredients of quantum mechanics. First, the Heisenberg/Schrodinger equation, an equation of motion…
We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum…
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the…
As known, the cylindrical gravitational field (wave) have been canonically quantized and its wave function, as the quantum one, interpreted in probability terms. We show in this work, using quantum Zeno methods, that this probability may be…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.
The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.