Related papers: The Quantum Relative Entropy as a Rate Function an…
In this paper we will give a short presentation of the quantum Levy-Khinchin formula and of the formulation of quantum continual measurements based on stochastic differential equations, matters which we had the pleasure to work on in…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on…
We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions and direct subadditivity arguments, as in the classical case,…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
The Renyi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Renyi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide…
We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we…
We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
Relative entropy serves as a cornerstone concept in quantum information theory. In this work, we study relative entropy of random states from major generic state models of Hilbert-Schmidt and Bures-Hall ensembles. In particular, we derive…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…