相关论文: Monotone Riemannian metrics on density matrices wi…

The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…

Since the seminal work by Beresteanu and Molinari(2008), the random set theory and related inference methods have been widely applied in partially identified econometric models. Meanwhile, there is an emerging field in statistics for…

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…

Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question…

We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…

The quantum measurement problem, understanding why a unique outcome is obtained in each individual experiment, is tackled by solving models. After an introduction we review the many dynamical models proposed over the years. A flexible and…

Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral…

Robert Bryant (Theorie des varietes minimales et applications, 1988, 154: 321-347) proved that an isolated singularity of a conformal metric of positive constant curvature on a Riemann surface is a conical one. Using Complex Analysis, we…

Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, but also the object of recent experimental quantum…

We prove that uniformly disconnected subsets of metric measure spaces with controlled geometry (complete, Ahlfors regular, supporting a Poincare inequality, and a mild topological condition) are contained in a quasisymmetric arc. This…

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…

The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…

The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…

We consider the following generalisation of a well-known problem in Riemannian geometry: When is a smooth real-valued function s on a given compact n-dimensional manifold M (with or without boundary) the scalar curvature of some smooth…

The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…

Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…