Related papers: Perturbation Bounds for Quantum Markov Processes a…
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
We propose a quantum mechanical method of detecting weak vibrational disturbances inspired by the protocol of entanglement farming. We consider a setup where pairs of atoms in their ground state are successively sent through an optical…
Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
Filter stability is a classical problem in the study of partially observed Markov processes (POMP), also known as hidden Markov models (HMM). For a POMP, an incorrectly initialized non-linear filter is said to be (asymptotically) stable if…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary…
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death…
In this paper, we consider a stabilization problem of an uncertain system in a networked control setting. Due to the network, the measurements are quantized to finite-bit signals and may be randomly lost in the communication. We study…
While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
In this paper, we consider the peak-covariance stability of Kalman filtering subject to packet losses. The length of consecutive packet losses is governed by a time-homogeneous finite-state Markov chain. We establish a sufficient condition…
Non-classical features of quantum systems can degrade when subjected to environment and noise. Here, we ask a fundamental question: What is the minimum amount of time it takes for a quantum system to exhibit non-classical features in the…
We present a general framework to study the metastability of random perturbations of dynamical systems. It integrates techniques from the theory of Markov processes, in particular the resolvent approach to metastability, with the spectral…
We present two new quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a…
In this paper we present some conditions for the (strong) stabilizability of an n-D Quantum MIMO system P(X). It contains two parts. The first part is to introduce the n-D Quantum MIMO systems where the coefficients vary in the algebra of…
We consider the apparatus in a quantum measurement process to be in a mixed state. We propose a simple upper bound on the probability of correctly distinguishing any number of mixed states. We use this to derive fundamental bounds on the…
We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…