Related papers: Belavkin-Staszewski Quantum Markov Chains
In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures…
We consider the problem of non degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains. We assume that starting from the state at higher energy the system necessarily visits…
Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an information critical phase as an extended region of a mixed state phase diagram where the Markov length,…
Product-form stationary distributions in Markov chains have been a foundational advance and driving force in our understanding of stochastic systems. In this paper, we introduce a new product-form relationship that we call "graph-based…
The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all…
We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however…
The issue of whether non-Markovianity (NM) could be considered as a resource in quantum information has been a subject of intense debate for the last years. Recently, a simple mechanism was proposed in which one of the main features of NM,…
We present a general method to characterize the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully-nonlocal according to a given partition, as well as being…
Recently in Ref.\cite{Wen:2021qgx}, one of the authors introduced the balanced partial entanglement (BPE), which has been proposed to be dual to the entanglement wedge cross-section (EWCS). In this paper, we explicitly demonstrate that the…
Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Physical…
In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available.…
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy…
We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case…
Despite its fully unitary dynamics, the bosonic Kitaev chain (BKC) displays key hallmarks of non-Hermitian physics including non-reciprocal transport and the non-Hermitian skin effect. Here we demonstrate another remarkable phenomena: the…
Starting from an arbitrary full-rank state of a lattice quantum spin system, we define a "canonical purified Hamiltonian" and characterize its spectral gap in terms of a spatial mixing condition (or correlation decay) of the state. When the…
We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system-environment…
It is believed that an isolated and far-from-equilibrium quantum many-body system should try to attain equilibrium via a mechanism whereby any given subsystem acts as an open quantum system that is coupled to an environment, which is the…
In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. To make this point more clear,…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
The model of multi-level open quantum system interacting with a non-vacuum reservoir in the rotating wave approximation is considered. We provide an exact integral representation for the reduced density matrix of the system. For identical…