Related papers: An Ergodic Theorem for Quantum Counting Processes
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for…
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…
For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdi\`ere and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we…
We introduce a quantum measurement process that is capable of characterizing an unknown state of a system almost without disturbing or collapsing it. The underlying idea is to extract information of a system from the thermodynamic…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…
A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure…
We undertake a detailed analysis of ergodicity for homogeneous discrete-time quantum walks on the integer lattice. The most significant result of our paper holds in dimension one, and gives a complete equivalence between the absolutely…
The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork…
We analyze the problem of a quantum computer in a correlated environment protected from decoherence by QEC using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
We formulate a minimal model of a quantum particle detector as an autonomous quantum thermal machine. Our goal is to establish how entropy production, which is needed to maintain the detector out of equilibrium, is linked to the quality of…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to…
Information spreads in time. For example, correlations dissipate when the correlated system locally couples to a third party, such as the environment. This simple but important fact forms the known quantum data-processing inequality. Here…