Related papers: Markov states on the CAR algebra
In the paper it is defined two marginal Markov processes on von Neumann algebras $\cm$ and $\cm\o\cm$, respectively, corresponding to given quantum quadratic stochastic process (q.q.s.p.). It is proved that such marginal processes uniquely…
The study of Markov models is central to control theory and machine learning. A quantum analogue of partially observable Markov decision process was studied in (Barry, Barry, and Aaronson, Phys. Rev. A, 90, 2014). It was proved that…
Although the security of quantum cryptography is provable based on the principles of quantum mechanics, it can be compromised by the flaws in the design of quantum protocols and the noise in their physical implementations. So, it is…
Markov processes play an important role in physics and the theory of open systems in particular. In this paper we study the asymptotic evolution of trace-nonincreasing homogenous quantum Markov processes (both types, discrete quantum Markov…
A set of Markov processes corresponding to systems of hard-core particles interacting along the line are shown to be solvable via a dynamic matrix product ansatz (DMPA). We show that quantum spin Hamiltonians can be treated by the DMPA as…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Markov decision processes continue to gain in popularity for modeling a wide range of applications ranging from analysis of supply chains and queuing networks to cognitive science and control of autonomous vehicles. Nonetheless, they tend…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
We continue the analysis of nontrivial examples of quantum Markov processes. This is done by applying the construction of entangled Markov chains obtained from classical Markov chains with infinite state--space. The formula giving the joint…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
We consider a class of quantum dissipative semigroup on a von-Neumann algebra which admits a normal invariant state. We investigate asymptotic behavior of the dissipative dynamics and their relation to that of the canonical Markov shift. In…
Markov chain models are used in various fields, such behavioral sciences or econometrics. Although the goodness of fit of the model is usually assessed by large sample approximation, it is desirable to use conditional tests if the sample…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
We derive an adiabatic theorem for Markov chains using well known facts about mixing and relaxation times. We discuss the results in the context of the recent developments in adiabatic quantum computation.
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
Topos quantum theory provides representations of quantum states as direct generalizations of the probability distribution, namely probability valuation. In this article, we consider extensions of a known bijective correspondence between…
We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…