Entanglement of positive definite functions on compact groups

We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of Horodecki Theorem, giving a necessary and sufficient criterion for separability of such functions. The resulting characterisation is given in terms of mappings of the space of continuous functions, preserving positive definiteness. The relation between the developed group-theoretical formalism and the conventional one, given in terms of density matrices, is established through the non-commutative Fourier analysis.Comment: published versio

Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition

We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the state-space of the system, achieving a unified quantum-classical language and a novel version of the correspondence principle. We briefly discuss the structure of observables and dynamics within our framework.Comment: final versio

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

Entanglement and Quantum Superposition of a Macroscopic - Macroscopic system

Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space - like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel Macro - Macro paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N=10^5 particles. Crucial experimental issues as the violation of Bell's inequalities by the Macro - Macro system are considered.Comment: 4 pages, 4 figure

Theoretical pathways towards experimental quantum simulators

Recent progress in quantum optics and quantum information has brought the long-standing dreams of quantum simulators and even quantum computers (almost) within reach. Here, we review some current theoretical pathways supporting experimental progress towards quantum simulators. In this, we focus mainly on topological aspects and numerical studies of quantum computation. © Sociedad Española de Óptica.This work was funding by the Spanish MEC projects TOQATA (FIS2008-00784), QOIT (Consolider Ingenio 2010), ACUTE, ERC Advanced Grant QUAGATUA, EU STREP NAMEQUAM, partly (E. Sz.) by the Hungarian Research Fund (OTKA) under Grant No. 68340, the Barcelona Supercomputing Center - Centro Nacional de Supercomputación (FI2008-3-0029, FI2009-1-0019) (A.N.), and Alexander von Humboldt Foundation (M.L.).Peer Reviewe