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Faculté des Sciences
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Entanglement Classification by Algebraic Geometry

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Weelen, Tom ULiège
Promotor(s) : Bastin, Thierry ULiège
Date of defense : 24-Jun-2021/25-Jun-2021 • Permalink : http://hdl.handle.net/2268.2/12230
Details
Title : Entanglement Classification by Algebraic Geometry
Translated title : [fr] Classification de l'Intrication par la Géométrie Algébrique
Author : Weelen, Tom ULiège
Date of defense  : 24-Jun-2021/25-Jun-2021
Advisor(s) : Bastin, Thierry ULiège
Committee's member(s) : Bousquet, Eric ULiège
Dorbolo, Stéphane ULiège
Martin, John ULiège
Mathonet, Pierre ULiège
Language : English
Number of pages : 80
Keywords : [en] Entanglement
[en] Entanglement Classification
[en] Entanglement classification by algebraic geometry
[en] Entanglement thesis
[en] entanglement classification thesis
[en] Algebraic geometry thesis
[en] algebraic geometry
[en] Intrication
[en] Classification de l'intrication
[en] Thesis about entanglement classification
[en] Gharahi
[en] Mancini
[en] Ottaviani
[en] k-secant
[en] tangent variety
[en] projective Hilbert space
[en] l-multilinear rank
[en] projective variety
[en] SLOCC classification
[en] SLOCC entanglement
[en] Classification algorithm
[en] Segre embedding
[en] Zariski topology
Discipline(s) : Physical, chemical, mathematical & earth Sciences > Physics
Research unit : Institut de Physique Nucléaire Atomique et Spectroscopique (IPNAS)
Target public : Researchers
Professionals of domain
Complementary URL : https://www.cesam.uliege.be/cms/c_5012589/fr/ipnas
Institution(s) : Université de Liège, Liège, Belgique
Degree: Master en sciences physiques, à finalité approfondie
Faculty: Master thesis of the Faculté des Sciences

Abstract

[en] The role of entanglement is to substantially enhance the speed of computations by a process that classical computers could not achieve. Indeed, entanglement is something mysterious from quantum mechanics that has no equivalent in classical mechanics. An enormous quantity of work has been carried in the past decades to answer some natural questions about entanglement. How to know if a state is entangled or not (Separability problem)? If a state is entangled, how much is it, and how far from a separable state is it (Entanglement measure)? Can an entangled state perform the same tasks as another entangled state (Entanglement classification)? These questions are increasingly mastered over time and are the keystone of progress in quantum computation, in conjunction with technical progress. Entanglement classification fails to be finite when we consider something greater than a 4-qubit system. This issue has been analysed and solved by Masoud Gharahi, Stefano Mancini and Giorgio Ottaviani in their paper with help of algebraic geometry. The purpose of this thesis is to make a detailed overview of the notions this article needs to be understood.


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  • Weelen, Tom ULiège Université de Liège > Master sc. phys., à fin.

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