Related papers: Quantum-mechanical probability from the symmetries…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
In the following paper, we generalize the geometrical framework of qubit decoherence to higher dimensions. The quantum mixed state is represented by the probability distribution, which is the K\"ahler function on the projective Hilbert…
To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D.Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D.Deutsch. The idea is to get subjective probabilities from…
We prove that the Hilbert space description of all joint von Neumann measurements on a quantum state can be reproduced in terms of a single measure space ({\Omega}, F, {\mu}) with a normalized real-valued measure {\mu}, that is, in terms of…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
The quantum de Finetti theorem says that, given a symmetric state, the state obtained by tracing out some of its subsystems approximates a convex sum of power states. The more subsystems are traced out, the better this approximation…
The probabilistic interpretation of quantum mechanics has been a point of discussion since the earliest days of the theory. The development of quantum technologies transfer these discussions from philosophical interest to practical…
A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.
Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
Modal quantum theory (MQT) is a "toy model" of quantum theory in which amplitudes are elements of a general field. The theory predicts, not the probabilities of a measurement result, but only whether or not a result is possible. In this…
Probably the simplest and most frequently used way to illustrate the power of quantum computing is to solve the so-called {\it Deutsch's problem}. Consider a Boolean function $f: \{0,1\} \to \{0,1\}$ and suppose that we have a (classical)…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New entropic--information inequalities are obtained for…