Related papers: Quantum query complexity of entropy estimation
We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures.…
Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we…
The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…
In a world where more decisions are made using artificial intelligence, it is of utmost importance to ensure these decisions are well-grounded. Neural networks are the modern building blocks for artificial intelligence. Modern neural…
In this paper we study certain properties of R\'{e}nyi entropy functionals $H_\alpha(\mathcal{P})$ on the space of probability distributions over $\mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties…
A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the…
A new sharp inequality featuring the differential R\'enyi entropy, the R\'enyi divergence and the R\'enyi cross-entropy of a pair of probability density functions is established. The equality is reached when one of the probability density…
Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as…
Quantitative information flow analyses (QIF) are a class of techniques for measuring the amount of confidential information leaked by a program to its public outputs. Shannon entropy is an important method to quantify the amount of leakage…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
The random variable simulation problem consists in using a $k$-dimensional i.i.d. random vector $X^{k}$ with distribution $P_{X}^{k}$ to simulate an $n$-dimensional i.i.d. random vector $Y^{n}$ so that its distribution is approximately…
The Renyi distribution ensuring the maximum of a Renyi entropy is investigated for a particular case of a power--law Hamiltonian. Both Lagrange parameters, $\alpha$ and $\beta$ can be excluded. It is found that $\beta$ does not depend on a…
We leverage the Gibbs inequality and its natural generalization to R\'enyi entropies to derive closed-form parametric expressions of the optimal lower bounds of $\rho$th-order guessing entropy (guessing moment) of a secret taking values on…
We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean $\mu$ of a distribution on $\mathbb{R}^d$ given $n$…
We propose R\'enyi information generating function and discuss its properties. A connection between the R\'enyi information generating function and the diversity index is proposed for discrete type random variables. The relation between the…
A realistic Quantum Key Distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
Sharpness (of the loss minima) is a common measure to investigate the generalization of neural networks. Intuitively speaking, the flatter the landscape near the minima is, the better generalization might be. Unfortunately, the correlation…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…