Rotationally invariant multipartite states

We construct a class of multipartite states possessing rotational SO(3) symmetry -- these are states of K spin-j_A particles and K spin-j_B particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.Comment: 18 pages; new reference

Long-range multipartite entanglement close to a first order quantum phase transition

We provide insight in the quantum correlations structure present in strongly correlated systems beyond the standard framework of bipartite entanglement. To this aim we first exploit rotationally invariant states as a test bed to detect genuine tripartite entanglement beyond the nearest-neighbor in spin-1/2 models. Then we construct in a closed analytical form a family of entanglement witnesses which provides a sufficient condition to determine if a state of a many-body system formed by an arbitrary number of spin-1/2 particles possesses genuine tripartite entanglement, independently of the details of the model. We illustrate our method by analyzing in detail the anisotropic XXZ spin chain close to its phase transitions, where we demonstrate the presence of long range multipartite entanglement near the critical point and the breaking of the symmetries associated to the quantum phase transition.Comment: 6 pages, 3 figures, RevTeX 4, the abstract was changed and the manuscript was extended including the contents of the previous appendix

Valence Bond States: Link models

An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott-Hubbard insulators is given by means of the two-point equal-time correlation function obtained i) numerically from the suggested state and ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.Comment: 20 pages, 15 figures; added references, corrected some typos, new sections. Published versio

Genuine quantum correlations in quantum many-body systems: a review of recent progress

Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.Comment: Review. Close to published version. Comments are welcome! Please write an email to g.dechiara[(at)]qub.ac.u

Classification of local realistic theories

Recently, it has shown that an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment (two-setting model), works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a {\it continuous-infinite} settings Bell experiment (infinite-setting model), even though there exist two-setting models for all directions in space. Hence, two-setting model does not have the property which infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in a {\it only discrete-three} settings Bell experiment (three-setting model), even though there exist two-setting models for the three measurement directions chosen in the given three-setting experiment. Hence, two-setting model does not have the property which three-setting model has.Comment: To appear in Journal of Physics A: Mathematical and Theoretica

Local discrimination of rotationally invariant states

Tesina realitzada en col.laboració al l'Universitat Autònoma de Barcelona. Facultat de CiènciesMàster oficial realitzat en col·laboració amb Universitat Autònoma de Barcelona (UAB), Universitat de Barcelona (UB) i Institut de Ciències Fotòniques (ICFO)We provide lower bounds for the minimum error discrimination probability of multipartite rotationally invariant states using separable measurements. The separability of the measurement operators has been investigated, and we have found PPT-based conditions which can be directly tested in the total angular momentum basis

Local discrimination of rotationally invariant states

Tesina realitzada en col.laboració al l'Universitat Autònoma de Barcelona. Facultat de CiènciesMàster oficial realitzat en col·laboració amb Universitat Autònoma de Barcelona (UAB), Universitat de Barcelona (UB) i Institut de Ciències Fotòniques (ICFO)We provide lower bounds for the minimum error discrimination probability of multipartite rotationally invariant states using separable measurements. The separability of the measurement operators has been investigated, and we have found PPT-based conditions which can be directly tested in the total angular momentum basis

Geometric Entanglement of Symmetric States and the Majorana Representation

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science (LNCS