Related papers: Generalized R\'enyi entropy accumulation theorem a…
We have formerly introduced Deep Random Secrecy, a new cryptologic technique capable to ensure secrecy as close as desired from perfection against unlimited passive eavesdropping opponents. We have also formerly introduced an extended…
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…
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an…
We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannon entropy is the special case $\eta=1$. The order of R\'enyi entropy is determined by the…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
Entropically secure encryption is a way to encrypt a large plaintext with a small key and still have information-theoretic security, thus in a certain sense circumventing Shannon's result that perfect encryption requires the key to be at…
In this work, maximal $\alpha$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an…
Shannon's fundamental bound for perfect secrecy says that the entropy of the secret message cannot be larger than the entropy of the secret key initially shared by the sender and the legitimate receiver. Massey gave an information theoretic…
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
Lower bounds for the R\'enyi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
Generating secure random numbers is a central problem in cryptography that needs a reliable source of enough computing entropy. Without enough entropy available - meaning no good source of secure random numbers - a device is susceptible to…
Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective…
We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in…