Related papers: Invariant Measure for Quantum Trajectories
In this paper, we study dynamical quantum networks which evolve according to Schr\"odinger equations but subject to sequential local or global quantum measurements. A network of qubits forms a composite quantum system whose state undergoes…
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…
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be…
In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-space Markov chains which are (possibly) not irreducible.…
Maximum likelihood estimation is applied to the determination of an unknown quantum measurement. The measuring apparatus performs measurements on many different quantum states and the positive operator-valued measures governing the…
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general…
We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a…
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
The Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…