相关论文: On a Time Symmetric Formulation of Quantum Mechani…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
Formulas for calculating the joint probability of outcomes of measurements performed on mutually non-interacting component systems of a combined system prepared in an entangled state are presented. The formulas are based on non-relativistic…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…
We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…
The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring…
We address the statistics of a simultaneous CWLM of two non-commuting variables on a few-state quantum system subject to a conditioned evolution. Both conditioned quantum measurement and that of two non-commuting variables differ…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
In this paper, without any priori assumption about the post-measurement state of system, we will examine how this state is restricted by assuming each of these following assumptions. First, by using this reasonable assumption that two…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…