Related papers: On the merit of a Central Limit Theorem-based appr…
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…
Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we…
We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…
The thermodynamic limit in statistical thermodynamics of many-particle systems is an important but often overlooked issue in the various applied studies of condensed matter physics. To settle this issue, we review tersely the past and…
The problem of estimating a parameter of a quantum system through a series of measurements performed sequentially on a quantum probe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. We present a…
A paradigm shift in quantum thermometry is proposed. To date, thermometry has relied on local estimation, which is useful to reduce statistical fluctuations once the temperature is very well known. In order to estimate temperatures in cases…
Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
We assess precision thermometry for an arbitrary single quantum system. For a $d$-dimensional harmonic system we show that the gap sets a single temperature that can be optimally estimated. Furthermore, we establish a simple linear…
Temperature of a finite-sized system fluctuates due to the thermal fluctuations. However, a systematic mathematical framework for measuring or estimating the temperature is still underdeveloped. Here, we incorporate the estimation theory in…
Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schr\"odinger's equation and the second law of thermodynamics. Despite…
It is "conventional wisdom" that the uncertainty of local temperature measurements on equilibrium systems diverges exponentially fast as their temperature $T$ drops to zero. In contrast, some exactly solvable models showcase a more benign…
We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse…
We present two recent works on the thermodynamic limit of quantum Coulomb systems, in which we provided a general method allowing to show the existence of the limit for many different models.
We consider the estimation of an unknown parameter $\theta$ through a quantum probe at thermal equilibrium. The probe is assumed to be in a Gibbs state according to its Hamiltonian $H_\theta$, which is divided in a parameter-encoding term…
The \textit{Central Limit Theorem (CLT)} is at the heart of a great deal of applied problem-solving in statistics and data science, but the theorem is silent on an important implementation issue: \textit{how much data do you need for the…
We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and \lambda is the…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…