Related papers: Measuring quantum relative entropy with finite-siz…
We investigate properties of the pseudo-Riemannian volume, entropy, and diameter for convex cocompact representations $\rho : \Gamma \to \mathrm{SO}(p,q+1)$ of closed $p$-manifold groups. In particular: We provide a uniform lower bound of…
In this work we calculate the Cram\'{e}r-Rao, the Fisher-Shannon and the L\'{o}pez-Ruiz-Mancini-Calbert (LMC) complexity measures for eigenstates of a deformed Schr\"{o}dinger equation, being this intrinsically linked with…
Let $\Omega$ be a bounded closed convex set in ${\mathbb R}^d$ with non-empty interior, and let ${\cal C}_r(\Omega)$ be the class of convex functions on $\Omega$ with $L^r$-norm bounded by $1$. We obtain sharp estimates of the…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…
We prove that the quantum relative entropy is a rate function in large deviation principle. Next, we define information criteria for quantum states and estimate the accuracy of the use of them. Most of the results in this paper are…
Recently, some attention has been given to the so-called Page-Wootters mechanism of quantum clocks. Among the various proposals to explore the mechanism using more modern techniques, some have chosen to use a quantum information…
In this article we study weighted sums of $n$ i.i.d. Gamma($\alpha$) random variables with nonnegative weights. We show that for $n \geq 1/\alpha$ the sum with equal coefficients maximizes differential entropy when variance is fixed. As a…
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We…
Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…
We present a novel strategy for obtaining optimal probe states and measurement schemes in a class of noiseless multiparameter estimation problems with symmetry among the generators. The key to the framework is the introduction of a set of…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
We show that an entanglement measure called relative entropy of entanglement satisfies a strong continuity condition. If two states are close to each other then so are their entanglements per particle pair in this measure. It follows in…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
In this paper, new methodology -- direct approach -- for the determination of the attainable CR type bound of the pure state model, is proposed and successfully applied to the wide variety of pure state models, for example, the…
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…