Related papers: Measuring quantum relative entropy with finite-siz…
The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…
Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…
This paper aims at providing a fresh look at semiparametric estimation theory and, in particular, at the Semiparametric Cram\'{e}r-Rao Bound (SCRB). Semiparametric models are characterized by a finite-dimensional parameter vector of…
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…
The author studies the Cram\'{e}r-Rao type bound by a linear programming approach. By this approach, he found a necessary and sufficient condition that the Cram\'{e}r-Rao type bound is attained by a random measurement. In a spin 1/2 system,…
We use large-$N$ diagrammatic techniques to calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. These methods are specifically designed for symmetric sectors, allowing us to determine the relative…
Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak…
We investigate strategies for reaching the ultimate limit on the precision of frequency estimation when the number of probes used in each run of the experiment is fixed. That limit is set by the quantum Cram\'er-Rao bound (QCRB), which…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm…
In quantum purity amplification, one is given $n$ copies of a noisy quantum state $\rho \in \mathbb{C}^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\rangle$. Several prior works have derived…
Shannon entropy is not the only entropy that is relevant to machine-learning datasets, nor possibly even the most important one. Traditional entropies such as Shannon entropy capture information represented by elements' frequencies but not…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
Let $\rho$ and $\mu$ be two probability measures on $\mathbb{R}$ which are not the Dirac mass at $0$. We denote by $H(\mu|\rho)$ the relative entropy of $\mu$ with respect to $\rho$. We prove that, if $\rho$ is symmetric and $\mu$ has a…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
Given an arbitrary quantum state ($\sigma$), we obtain an explicit construction of a state $\rho^*_\varepsilon(\sigma)$ (resp. $\rho_{*,\varepsilon}(\sigma)$) which has the maximum (resp. minimum) entropy among all states which lie in a…
Relative entropy serves as a cornerstone concept in quantum information theory. In this work, we study relative entropy of random states from major generic state models of Hilbert-Schmidt and Bures-Hall ensembles. In particular, we derive…