Elements of Non Classicality in Multi Level Systems

Abstract

Quantum physics has struck a chord in the field of information theory due to non-classical features newlinesuch as entanglement and non-locality, giving rise to applications that are otherwise impossible in newlinethe classical context. While numerous studies have been conducted and applications established for newlinetwo-level systems, that is, qubit systems, much less has been accomplished for more complicated, newlinehigher level systems, which may prove more powerful for applications in cryptography, memory, newlineand communication. Moreover, alternative detectors of non-classicality remain to be thoroughly newlineexplored. newlineIt is thus pertinent to study higher level systems on top of thoroughly studied qubit systems, newlinealong with alternative potential resources for non-classical information theoretic purposes. This newlinethesis is an attempt in that direction, as a study of non-classicality in multi-level systems not newlineonly for more common quantum resources, but in the light of new, promising resources as well. newlineFirst, the notion of a weak classical limit is proposed, reconciling two seemingly contradictory newlineresults: that of classicality in the large N limit, and thriving non-locality and entanglement in newlinehigher level systems. Next, a detailed comparative study is performed between two prominent newlinedetectors of non-locality: the CGLMP and Bell-CHSH inequalities. Thirdly, a unified framework newlinefor detecting non-classicality based on non-classical probabilities, called the pseudo-probability newlineformalism, previously established for qubit systems, is extended to single qutrit systems. newlineThe approaches followed to study various aspects of non-classicality culminate with the proposal newlineof a secure state-independent quantum key distribution (SIQKD) protocol. It is hoped that newlinethis thesis will provide a good basis for the elements of non-classicality in multi-level systems, newlinewhile paving the way for state-independent quantum information theoretic protocols newline