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We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of…
Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, then the value of the Shannon entropy comes to formally…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
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…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
It was recently demonstrated that a multitude of realizations of several magnetic sensing technologies satisfy the energy resolution limit, which connects a quantity composed by the variance of the magnetic field estimate, the sensor volume…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters…
Knowing about optimal quantum measurements is important for many applications in quantum information and quantum communication. However, deriving optimal quantum measurements is often difficult. We present a collection of results for…
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…
We identify the optimal measurement for obtaining information about the original quantum state after the state to be measured has undergone partial decoherence due to noise. We quantify the information that can be obtained by the…
We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein's equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of…
We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang…
The purpose of this article is to exploit the geometric structure of Quantum Mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that…
Quantum metrology research promises approaches to build new sensors that achieve the ultimate level of precision measurement and perform fundamentally better than modern sensors. Practical schemes that tolerate realistic fabrication…
Quantum metrology concerns improving the estimation of an unknown parameter using an optimal measurement scheme on the quantum system. More the optimality of the measurement, the better will be the improvement in sensing the value of the…
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via…
The quantification and classification of quantum entanglement is a very important and still open question of quantum information theory. In this paper, we describe an entanglement measure for multipartite pure states (the minimum of…
We discuss thermodynamic work cost of various stages of a quantum estimation protocol: probe and memory register preparation, measurement and extraction of work from post-measurement states. We consider both (i) a multi-shot scenario, where…
Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is an extensive debate over the question how the sensitivity scales with the resources (such as the average photon number) and…