Entanglement, Einstein-Podolsky-Rosen steering and cryptographical applications

Kogias, Ioannis (2016) Entanglement, Einstein-Podolsky-Rosen steering and cryptographical applications. PhD thesis, University of Nottingham.

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Abstract

This PhD Dissertation collects results of my own work on the topic of continuous variable (CV) quantum teleportation, which is one of the most important applications of quantum entanglement, as well as on the understanding, quantification, detection, and applications of a type of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering, for both bipartite and multipartite systems and with a main focus on CV systems.

For the first results, we examine and compare two fundamentally different teleportation schemes; the well-known continuous variable scheme of Vaidman, Braunstein and Kimble, and a recently proposed hybrid scheme by Andersen and Ralph. We analyse the teleportation of ensembles of arbitrary pure single-mode Gaussian states using these schemes and compare their performance against classical strategies that utilize no entanglement (benchmarks). Our analysis brings into question any advantage due to non-Gaussianity for quantum teleportation of Gaussian states.

For the second part of the results, we study bipartite EPR-steering. We propose a novel powerful method to detect steering in quantum systems of any dimension in a systematic and hierarchical way. Our method includes previous results of the literature as special cases on one hand, and goes beyond them on the other. We proceed to the quantification of steering-type correlations, and introduce a measure of steering for arbitrary bipartite Gaussian states, prove many useful properties, and provide with an operational interpretation of the proposed measure in terms of the key rate in one-sided device independent quantum key distribution. Finally, we show how the Gaussian steering measure gives a lower bound to a more general quantifier of which Gaussian states are proven to be extremal.

We proceed to the study of multipartite steering, and derive laws for the distribution of Gaussian steering among different parties in multipartite Gaussian states. We define an indicator of collective steering-type correlations, which is interpreted operationally in terms of the guaranteed secret key rate in the multi-party cryptographic task of quantum secret sharing.

The final results look at the cryptographical task of quantum secret sharing, whose security has remained unproven almost two decades after its original conception. By utilizing intuition and ideas from steering, we manage to establish for the first time an unconditional security proof for CV entanglement-based quantum secret sharing schemes, and demonstrate their practical feasibility. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Adesso, Gerardo
Fuentes, Ivette
Keywords: quantum mechanics, entanglement, quantum information, quantum cryptography, quantum teleportation, steering, einstein-podolsky-rosen paradox, EPR paradox, einstein-podolsky-rosen steering, EPR steering, continuous variables, steering detection, Gaussian, steering measures, steering quantifiers, multipartite steering, monogamy, secret sharing, device independent
Subjects: Q Science > QA Mathematics > QA150 Algebra
Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 34584
Depositing User: Kogias, Ioannis
Date Deposited: 03 Feb 2017 13:06
Last Modified: 03 Feb 2017 13:15
URI: http://eprints.nottingham.ac.uk/id/eprint/34584

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