相关论文: Nonadditive generalization of the quantum Kullback…

We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…

Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be…

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability…

We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…

Quantum state discrimination depicts the general progress of extracting classical information from quantum systems. We show that quantum state discrimination can be realized in a device-independent scenario using tools of self-testing…

Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized…

In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows…

In quantum learning tasks, quantum memory can offer exponential reductions in statistical complexity compared to any single-copy strategies, but this typically necessitates at least doubling the system size. We show that such exponential…

The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…

We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically…

The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix,…

Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum…

A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…

Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…

We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric on the space of density matrices as the complexity measure. Due to Uhlmann's theorem, we…

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of…

We derive a closed form solution for the Kullback-Leibler divergence between two generalized gamma distributions. These notes are meant as a reference and provide a guided tour towards a result of practical interest that is rarely…

Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…