Related papers: Probabilities in the logic of quantum propositions
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
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 having it follow from…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
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…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theory's inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum state's…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
There is a significant body of literature, which includes Itamar Pitowksy's "Betting on Outcomes of Measurements," that sheds light on the structure of quantum mechanics, and the ways in which it differs from classical mechanics, by casting…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the…
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 fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective…
Within quantum mechanics it is possible to assign a probability to the chance that a measurement has been made at a specific time t. However, the interpretation of such a probability is far from clear. We argue that a recent measuring…
We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to…
Quantum correlations and other phenomena characteristic to a quantum world can be understood as simply consequences of a principle derived from the postulates of Quantum Mechanics. This explanatory principle states that these phenomena…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…