Related papers: Quantum Markov Chains: A unification approach

This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…

We introduce a Markov chain model of concurrent quantum programs. This model is a quantum generalization of Hart, Sharir and Pnueli's probabilistic concurrent programs. Some characterizations of the reachable space, uniformly repeatedly…

Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…

We present an implementation of Quantum Computing for a Markov Chain Monte Carlo method with an application to cosmological functions, to derive posterior distributions from cosmological probes. The algorithm proposes new steps in the…

We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…

We propose a universal framework for classifying quantum states based on their scale-resolved correlation structure. Using the recently introduced information lattice, which provides an operational definition of the total amount of…

Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…

The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…

We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain…

The program relative to the investigation of quantum Markov states for spin chains based on Canonical Anticommutation Relations algebra is carried on. This analysis provides a further step for a satisfactory theory of quantum Markov…

Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and interacting Fock spaces (IFS) using the quantum probabilistic…

This paper studies uniqueness and nonuniqueness for potential reconstruction from one boundary measurement in quantum fields, associated with the steady state Schr\"{o}dinger equation. A uniqueness theorem of the inverse problem is…

In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by…

This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen…

The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…

We recast quantum entanglement as a cohomological obstruction to reconstructing a global quantum state from locally compatible information. We address this by considering presheaf cohomologies of states and entanglement witnesses.…

Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…

Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…

While the standard approach to quantum systems studies length preserving linear transformations of wave functions, the Markov picture focuses on trace preserving operators on the space of Hermitian (self-adjoint) matrices. The Markov…

General Markov chains in an arbitrary phase space are considered in the framework of the operator treatment. Markov operators continue from the space of countably additive measures to the space of finitely additive measures. Cycles of…