Related papers: Quantum Markov States on Cayley trees
We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values $0,1,\ldots,m,$ $m\geq2,$ and nonzero external field, on a Cayley tree of degree $k$ (with $k+1$ neighbors). We are aiming to extend the results of…
By introducing a quantitative `degree of commutativity' in terms of the angle between spin-observables we present two tight quantitative trade-off relations in the case of two qubits: First, for entangled states, between the degree of…
We consider the ferromagnetic n.n Ising model on Cayley trees in absence of external fields submitted to a modified majority rule transformation with overlapping cells already known to lead to non-Gibbsian measures. We describe the…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
In the present paper the Ising model with competing binary $J$ and $J_1$ interactions with spin values $\pm 1$, on a Cayley tree is considered. We study translation-invatiant Gibbs measures and corresponding free energies ones.
States of a generic quantum field theory on a curved spacetime are considered which satisfy the KMS condition with respect to an evolution associated with a complete (Killing) vector field. It is shown that at any point where the vector…
Recently, there has been significant interest in understanding the properties of Markov random fields (M.r.f.) defined on the independent sets of sparse graphs. When these M.r.f. are restricted to pairwise interactions (i.e. hardcore…
Gaussian quantum Markov semigroups (GQMSs) are of fundamental importance in modelling the evolution of several quantum systems. Moreover, they represent the noncommutative generalization of classical Orsntein-Uhlenbeck semigroups;…
We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated…
Characterizing multipartite quantum correlations beyond two parties is of utmost importance for building cutting edge quantum technologies, although the comprehensive picture is still missing. Here we investigate quantum correlations (QCs)…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Using extensive numerical analysis of 20,000 randomly generated two-qubit states, we provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI). Our systematic study shows…
We introduce the notion of Quasi-Stationary State (QSS) in the context of quantum Markov semigroups that generalizes the one of quasi-stationary distribution in the case of classical Markov chains. We provide an operational interpretation…
In this paper we construct several models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 2$. We prove that each of the constructed model has at least two translational-invariant…
For quantum phases of Hamiltonian ground states, the energy gap plays a central role in ensuring the stability of the phase as long as the gap remains finite. We propose Markov length, the length scale at which the quantum conditional…
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…
Recently by Rozikov an Ising model with competing interactions and spin values $\pm 1$, on a Cayley tree of order $k\geq 1$ has been considered and the ground states of the model are described. In this paper we describe some weak periodic…
In the present paper we provide a new construction of measure, called $p$-adic quasi Gibbs measure, for countable state of $p$-adic Potts model on the Cayley tree. Such a construction depends on a parameter $\frak{p}$ and wights. In…
We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of…
Sampling from Gibbs states -- states corresponding to system in thermal equilibrium -- has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers,…