Related papers: Quantum Markov Processes (Correspondences and Dila…
A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure…
The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition…
It has been found that Markovian quantum dissipative processes, described by the Lindblad equation, may have attractive steady-state manifolds, in which dissipation and decoherence can play a positive role to quantum information processing.…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We develop a qualitative theory of Markov Decision Processes (MDPs) and Partially Observable MDPs that can be used to model sequential decision making tasks when only qualitative information is available. Our approach is based upon an…
We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in [1-3]…
We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
For Cox processes we construct a Markov process with increasing paths to couple the condensations of the Cox process in a monotone way. A similar procedure procedure yields an analogue Markov process for the P\'olya sum process. Moreover,…
We show that quantum dynamical systems can exhibit infinite correlations in their behavior when repeatedly measured. We model quantum processes using quantum finite-state generators and take the stochastic language they generate as a…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
The process of multicomponent condensation is considered. The theory taking into account several channels of nucleation is constructed. The analytical approximate description of the whole condensation process is given. The specific…
In this review we give a brief overview of quantum simulation as applied to the study of complex systems. In particular, we cover the basic ideas of quantum simulation, neuromorphic computation, the Sachdev-Ye-Kitaev model, as well as…
Engineering quantum systems offers great opportunities both technologically and scientifically for communication, computation, and simulation. The construction and operation of large scale quantum information devices presents a grand…
The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental…
We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a…
In this paper, we study Markov dynamics on unitary duals of compact quantum groups. We construct such dynamics from characters of quantum groups. Then we show that the dynamics have generators, and we give an explicit formula of the…
We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…