Related papers: Generalized R\'enyi entropy accumulation theorem a…
Quantum key distribution requires tight and reliable bounds on the secret key rate to ensure robust security. This is particularly so for the regime of finite block sizes, where the optimization of generalized R\'enyi entropic quantities is…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
The entropy accumulation theorem states that the smooth min-entropy of an $n$-partite system $A = (A_1, \ldots, A_n)$ is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are…
We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version,…
We present a comprehensive software framework for the finite-size security analysis of quantum random number generation (QRNG) and quantum key distribution (QKD) protocols, based on the Entropy Accumulation Theorem (EAT). Our framework…
This paper presents an enhanced post-quantum key agreement protocol based on R\'{e}nyi entropy, addressing vulnerabilities in the original construction while preserving information-theoretic security properties. We develop a theoretical…
Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its…
An important goal in quantum key distribution (QKD) is the task of providing a finite-size security proof without the assumption of collective attacks. For prepare-and-measure QKD, one approach for obtaining such proofs is the generalized…
Finite-size general security proofs for quantum key distribution based on R\'enyi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations…
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…
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterised, i.e.…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
Consider a sequential process in which each step outputs a system $A_i$ and updates a side information register $E$. We prove that if this process satisfies a natural "non-signalling" condition between past outputs and future side…
Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…
Will further scaling up of machine learning models continue to bring success? A significant challenge in answering this question lies in understanding generalization gap, which is the impact of overfitting. Understanding generalization gap…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the…
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…