Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

1. Front Matter

   Pages i-xxv

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2. Introduction

   • Jordi Tura i Brugués

   Pages 1-11

3. Background

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   Pages 13-35

4. PPT Entangled Symmetric States

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   Pages 37-72

5. Nonlocality in Multipartite Quantum States

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   Pages 73-137

6. Relating Entanglement and Nonlocality

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   Pages 139-155

7. Atomic Monogamies of Correlations

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   Pages 157-182

8. Conclusions and Outlook

   • Jordi Tura i Brugués

   Pages 183-188

9. Back Matter

   Pages 189-237

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This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel, experimentally friendly method to detect nonlocal correlations in many-body systems; the non-equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that some of these questions become tractable for such systems.

• Nonlocality in Many-Body Quantum Systems
• Entanglement Characterization
• Monogamies of Correlations
• Entanglement Witnesses
• Multipartite PPT
• Symmetry Constraints on Quantum Correlations
• Bell Correlations in Multipartite Systems
• PPT Symmetric Qubits
• Two-Body Correlators

• ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain

  Jordi Tura i Brugués

Dr. Jordi Tura i Brugués graduated simultaneously in Mathematics and Telecommunication Engineering at the Polytechnic University of Catalonia, under an intensive program offered by the Center for Interdisciplinary Studies. He obtained his PhD at ICFO - The Institute of Photonic Sciences, working in the Quantum Optics Theory group, under the supervision of Prof. Dr. Maciej Lewenstein and Dr. Remigiusz Augusiak. His research there focused on the characterization of entanglement and quantum correlations under symmetries. Currently, he is working as a postdoctoral researcher in the Theory Division of the Max Planck Institute of Quantum Optics in Garching, with Prof. Dr. Ignacio Cirac.