Related papers: Classical and quantum conditional measures from a …
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
The interrelation between classicality/quantumness and symmetry of states is discussed within the phase-space formulation of finite-dimensional quantum systems. We derive representations for classicality measures…
Model interactions between classical and quantum systems are briefly reviewed. These include: general measurement - like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, piecewise deterministic Markov processes…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how…
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…
We introduce quantum versions of Manin pairs and Manin triples and define quantum moment maps in this context. This provides a framework that incorporates quantum moment maps for actions of Lie algebras and quantum groups for any quantum…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
We study the mathematical structure of the notion of measurement space, which extends aspects of noncommutative topology that are based on quantale theory. This yields a geometric model of physical measurements that provides a realist…