Related papers: Chain rules for conditional entropies in quantum c…
It is repeatedly and persistently claimed in the literature that a specific trace criterion $d$ would guarantee universal composition security in quantum cryptography. Currently that is the sole basis of unconditional security claim in…
This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs…
Quantum security improves cryptographic protocols by applying quantum mechanics principles, assuring resistance to both quantum and conventional computer attacks. This work addresses these issues by integrating Quantum Key Distribution…
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…
Device-independent quantum cryptographic schemes aim to guarantee security to users based only on the output statistics of any components used, and without the need to verify their internal functionality. Since this would protect users…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
This thesis reports progress in two domains, causal structures and microscopic thermodynamics, both of which are pertinent in the development of quantum technologies. The first part is dedicated to the analysis of causal structure, which…
Quantum physical layer security protocols offer significant advantages, particularly in space communications, but their achievable secrecy rates are often limited to the asymptotic regime. Realistic communication systems, however, demand…
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…
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal 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…
We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and…
The uncertainty principle is one of the key concepts in quantum theory. This principle states that it is not possible to measure two incompatible observables simultaneously and accurately. In quantum information theory, the uncertainty…
The laws of quantum mechanics allow unconditionally secure key distribution protocols. Nevertheless, security proofs of traditional quantum key distribution (QKD) protocols rely on a crucial assumption, the trustworthiness of the quantum…
Many quantum phases, from topological orders to superfluids, are destabilized at finite temperature by the proliferation and motion of topological defects such as anyons or vortices. Conventional protection mechanisms rely on energetic gaps…
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be ($\tau$-)recurrent if every trajectory that starts in the set returns to it (within at most $\tau$ units of time).…
It is well established that the notion of min-entropy fails to satisfy the \emph{chain rule} of the form $H(X,Y) = H(X|Y)+H(Y)$, known for Shannon Entropy. Such a property would help to analyze how min-entropy is split among smaller blocks.…
It is well known that n bits of entropy are necessary and sufficient to perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be approximate, the amount of entropy needed doesn't asymptotically change. However, this is…
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural…
We find that the generally accepted security criteria are flawed for a whole class of protocols for quantum cryptography. This is so because a standard assumption of the security analysis, namely that the so-called square-root measurement…