Related papers: Diagonal Couplings of Quantum Markov Chains
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
We present a novel generalization of the chain mapping technique that applies to multi-atom, multimode systems by making use of coupling matrix transformations. This is extremely useful for tensor network simulations of multimode Dicke…
We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the…
One-shot coupling is a method of bounding the convergence rate between two copies of a Markov chain in total variation distance, which was first introduced by Roberts and Rosenthal and generalized by Madras and Sezer. The method is divided…
This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased…
The quantification of the entanglement present in a physical system is of para\-mount importance for fundamental research and many cutting-edge applications. Currently, achieving this goal requires either a priori knowledge on the system or…
This paper presents a self-contained account for coupling arguments and applications in the context of Markov processes. We first use coupling to describe the transport problem, which leads to the concepts of optimal coupling and…
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and…
In this note, we realize the half-steps of a general class of Markov chains as alternating projections with respect to the reverse Kullback-Leibler divergence between convex sets of joint probability distributions. Using this…
We recently showed that multipartite correlations between outcomes of random observables detect quantum entanglement in all pure and some mixed states. In this followup article we further develop this approach, derive a maximal amount of…
Entanglement between particle and detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine…
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed…
We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits…
The concept of balance between two state preserving quantum Markov semigroups on von Neumann algebras is introduced and studied as an extension of conditions appearing in the theory of quantum detailed balance. This is partly motivated by…
We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such…
We prove a noncommutative $(p,p)$-Poincar\'e inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap. Extending semi-commutative results of Huang and Tropp, our…
We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $\beta_m$ (if the sampled parts are…
We demonstrate how robust entanglement of quantum dot molecular system in a voltage controlled junction can be generated. To improve the quantum information characteristics of this system, we propose an applicable protocol which contains…
There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…
The first aim of this paper is to introduce a class of Markov chains on $\mathbb{Z}_+$ which are discrete self-similar in the sense that their semigroups satisfy an invariance property expressed in terms of a discrete random dilation…