相关论文: Reverse estimation theory, Complementality between…

Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we…

We use a R\'enyi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum or classical communication between two parties. These include state redistribution,…

In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…

An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…

Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event…

We introduce a pair of transformations, which are mutually inverse, acting on rather general classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as p-moments,…

Given a pure state vector |x> and a density matrix rho, the function p(x|rho)=<x|rho|x> defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to…

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity…

Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…

This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the…

Relative temporal-difference (TD) learning was introduced to mitigate the slow convergence of TD methods when the discount factor approaches one by subtracting a baseline from the temporal-difference update. While this idea has been studied…

As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In…

We propose a reformulation of quantum field theory (QFT) as a relativistic statistical field theory. This rewriting embeds a collapse model within an interacting QFT and thus provides a possible solution to the measurement problem.…

In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time…

Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty,…

Morozova and Chentsov (Morozova and Chentsov 90) studied Riemannian metrics on the set of probability measures. They showed that, up to a constant factor, the Fisher information is the only Riemannian metric which is monotone under…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

We study a proper definition of R\'enyi mutual information (RMI) in quantum field theory as defined via the Petz R\'enyi relative entropy. Unlike the standard definition, the RMI we compute is a genuine measure of correlations between…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…