Related papers: Marginal-constrained entropy accumulation theorem

In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched R\'enyi divergences such as the sandwiched R\'enyi conditional entropy. We follow three different approaches: The first one is the "almost…

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the…

We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…

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 describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed…

We introduce a new framework for quantum channel discrimination in an adversarial setting, where the tester plays against an adversary. We show that in asymmetric hypothesis testing, the optimal type-II error exponent is precisely…

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…

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…

A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…

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…

Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish…

Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…

The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. There is a certain perspective that the most fundamental notion in quantum mechanics…

We introduce a novel generalization of entropy and conditional entropy from which most definitions from the literature can be derived as particular cases. Within this general framework, we investigate the problem of designing…

We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not…

The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…

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.…

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…