Coupling of the system to its environment inevitably leads to the generation of system-bath correlations. Such correlations are often thought to be negligible in the weak-coupling Markovian regime. This is because the Markovian master equations are commonly derived using Born approximation that assumes factorization of the system-bath state. However, recent numerical studies have demonstrated...
The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states, and which is called a quantum trajectory. When the system under consideration is finite dimensional, and under some natural assumption related to the non-existence of so-called dark subspaces, the state of the system tends to become pure along the trajectory, a...
I will review some exactly solvable cases of classical deterministic and quantum unitary interacting 1D lattices driven by stochastic reservoirs at the ends. While in most cases the steady state can be written in terms of a homogeneous matrix product ansatz, I will outline a few situations where a compact inhomogeneous ansatz is needed.
Quantum trajectories arise when we couple a quantum system to a sequence of ancillas consecutively, and perform von Neumann measurements on the ancillas. Let the average evolution of the system be described by a semigroup ($T^n$). Then the ergodic components of the random outcome sequence are in one-to-one correspondence with the minimal projections in the center of the Kraus algebra of...
Quantum trajectories are Markov chains modeling the evolution of a quantum system subject to repeated indirect measurements. It was shown by Kümmerer and Maassen that, asymptotically, a quantum trajectory performs a random walk between the so-called `dark subspaces'. We show that this random walk admits a unique invariant probability measure and that the convergence towards this measure is...
Quantum systems typically reach thermal equilibrium when in weak contact with a large external bath. Understanding the speed of this thermalisation is a challenging problem, especially in the context of quantum many-body systems where direct calculations are intractable. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator, but this...
We provide an expression of the entropy production associated to a Markovian quantum dynamics defined by Lebowitz and Spohn, in terms of the two-time measurement protocol of the entropy observable, according to Kurchan. We do so under the detailed balance condition and, as a byproduct, we show that the probabilities of outcomes of two-time measurements are given by a continuous time Markov...
When we aim to accurately simulate the behaviour of complex and networked dynamical systems, the problem of finding simpler representations for the model of interest becomes critical. We focus on completely-positive dynamics, which can be used to describe a wide variety of relevant systems for quantum and classical information, including quantum walks and open systems, as well as classical...
We introduce a construction of Dirichlet forms on von Neumann algebras M associated to any eigenvalue of the Araki modular Hamiltonian of a f. n. non-tracial state, providing also conditions by which the associated Markovian semigroups are GNS symmetric. The structure of these Dirichlet forms is described in terms of unbounded spatial derivations, coercivity bounds are proved and the spectral...
We first introduce GQMS, describe the GKLS structure of their generators and briefly discuss their structure and some issues related with invariant states. Then we consider some special 2-mode system with quadratic Hamiltonian in creation and annihilation operators in which each mode interacts with a reservoir.
We show that any initial state converges to a certain stationary state whose the...
The estimation of an unknown parameter in quantum mechanical systems is a fundamental task for practical applications regarding quantum technologies. In the typical metrological scenario the unknown parameter is encoded in the state of n probes via local unitary operators; if the initial state is suitably engineered, one can estimate the parameter with a mean square error of the order of 1/n^2...
In this presentation I will discuss the problem of estimating dynamical parameters of a quantum Markov chain. The key tool will be the use of a coherent quantum absorber which transforms the problem into a simpler one pertaining to a system with a pure stationary state at a reference parameter value. Motivated by the proposal in [1] I will consider counting output measurements and show how the...
We investigate quantum channels, and in general quantum Markov evolutions, employing a probabilistic approach. Our interest is to study and analyze a systematic extension of the classical Markov chain theory into the quantum realm, a subject that has seen significant contributions from multiple authors in the past two decades. This seminar will specifically address absorption probabilities...
This talk and the following one form a series.
In this first talk we review the notion of entropy production of classical dynamical system based on the phase space contraction rate and discuss classical Evans-Searles and Gallavotti-Cohen fluctuation theorems. The passage to quantum mechanics by direct quantization of phase space contraction rate via modular theory runs into difficulties that...
Quantum trajectories are Markov chains modeling the evolution of a quantum system under repeated indirect measurements. The goal of this talk is to show how to prove limit theorems for these Markov chains. In particular, we show that the Markov operator associated to the Markov chain has a spectral gap, and we show that there exists an analytic perturbation of this operator. Then, by applying...
This talk is the continuation of the previous one.
In this second talk the two times quantum measurement entropy production is introduced. We will discuss a surprising stability result regarding statistics of this entropy production that impacts the respective quantum Evans-Searles and Gallavotti-Cohen fluctuation theorem. Finally, we will also discuss the ancilla state tomography that gives...
Several symmetry conditions have been introduced to describe the dissipative part of a quantum Markov semigroup in detailed balance, most prominently the GNS and KMS symmetry condition. I will give an overview over recent results concerning the generators of GNS-symmetric and KMS-symmetric quantum Markov semigroups on arbitrary von Neumann algebras and their connections to derivations,...
