Related papers: On Noncommutative Joinings
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…
The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of…
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \cite{1}. I treat some classical systems with various potentials and some Physical…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
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…
Correlations between the parts of a many-body system, and its time dynamics, lie at the heart of sciences, and they can be classical as well as quantum. Quantum correlations are traditionally viewed as constituted out of classical…
We address asymptotic decoupling in the context of Markovian quantum dynamics. Asymptotic decoupling is an asymptotic property on a bipartite quantum system, and asserts that the correlation between two quantum systems is broken after a…
We study the notion of joinings of W*-dynamical systems, building on ideas from measure theoretic ergodic theory. In particular we prove sufficient and necessary conditions for ergodicity in terms of joinings, and also briefly look at…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…
Recently some authors have pointed out that there exist nonclassical correlations which are more general, and possibly more fundamental, than entanglement. For these general quantum correlations and their classical counterparts, under the…
This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels…
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system.…
Since their introduction by Furstenberg in 1967, joinings have proved a very powerful tool in ergodic theory. We present here some aspects of the use of joinings in the study of measurable dynamical systems, emphasizing on - the links…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein's criterion for strong mixing are also discussed in this…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…