Bonjour à tous,

Vous êtes cordialement invité.e.s à la soutenance de thèse de Ashutosh Marwah, le vendredi 24 janvier 2025 à 13h30. La présentation sera offerte en anglais.

Jury

Résumé:

"One-shot information theory studies communication and information processing tasks under minimal structure, which is crucial for analysing scenarios with limited resources and cryptographic protocols. While the von Neumann entropy and its derivatives characterise rates in the asymptotic setting with i.i.d. structure, the one-shot regime requires a multitude of different entropic measures. One of the most important among these is the smooth min-entropy. In contrast to the von Neumann entropy, the behaviour of the smooth min-entropy is often unintuitive and restrictive, making it challenging to analyse structures that naturally arise in information theory.

This thesis focuses on 'approximation chains' - sequences of states which approximate the marginals of a quantum state. These structures naturally emerge when incorporating approximations in entropic identities, studying imperfections, and developing security proofs. While the von Neumann entropy of a state can be readily bounded through its approximation chain states, it is generally not possible to do so with the smooth min-entropy. We develop novel techniques for establishing smooth min-entropy bounds with approximation chains and demonstrate their applications in cryptographic scenarios."