## Characterizing Entanglement and Quantum Correlations Constrained by SymmetryThis 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. |

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### Contents

1 | |

13 | |

3 PPT Entangled Symmetric States | 36 |

4 Nonlocality in Multipartite Quantum States | 73 |

5 Relating Entanglement and Nonlocality | 139 |

6 Atomic Monogamies of Correlations | 156 |

7 Conclusions and Outlook | 183 |

Appendix A SchurWeyl Duality | 189 |

Appendix B Additional Proofs | 199 |

Appendix C Tables | 225 |

Appendix D Curriculum Vitae | 232 |

### Other editions - View all

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry Jordi Tura i Brugués No preview available - 2016 |

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry JORDI. TURA I BRUGUES No preview available - 2018 |

### Common terms and phrases

A.B. Sainz Acín Alice and Bob Augusiak Bell experiment Bell inequality Bell scenario Bell’s bipartition characterization consider convex combination convex set corresponding decomposition defined density matrix detect nonlocality Dicke elements entangled symmetric entanglement and nonlocality entanglement witnesses expectation value function given Hence Hidden Variable Hilbert space Horodecki implies inequivalent introduced irreps ISSN Lett Lewenstein LHVM linear maps matrix maximal quantum violation maximal violation measurements monogamy relations no-signalling nonlocal correlations nonlocality in many-body number of parties observables obtain optimal outcomes parameters performed permutation permutationally invariant Phys physical Pironio polytope POVMs PPT entangled PPT symmetric PPTESS probability distribution product vectors Proof Quantum Correlations quantum information quantum information theory Quantum Key Distribution qubits randomness representation result separable subspace subsystems Theorem theory translationally invariant Tur+14a Tura two-body correlators vertices