Entanglement of high-dimensional quantum systems has become increasingly important for quantum communication and experimental tests of nonlocality. However, many effects of highdimensional entanglement can be simulated by using multiple copies of low-dimensional systems. We present a general theory to characterize those high-dimensional quantum states for which the correlations cannot simply be simulated by low-dimensional systems. Our approach leads to general criteria for detecting multilevel entanglement in multiparticle quantum states, which can be used to verify these phenomena experimentally.
We generalize the class of hypergraph states to multipartite systems of qudits, by means of constructions based on the d-dimensional Pauli group and its normalizer. For simple hypergraphs, the different equivalence classes under local operations are shown to be governed by a greatest common divisor hierarchy. Moreover, the special cases of three qutrits and three ququarts is analysed in detail.
On September 6, 2001, Professor Fernando Valderrabano (Hospital Gregorio Marañon, Madrid) died at the age of 59 years. He was a leading figure in Spanish nephrology, a full professor of Medicine/Nephrology at the University Complutense of Madrid, and an outstanding scientist who published more than 300 articles in medical journals. He was a very intelligent and cultured person, and a man of great style who enjoyed a wide range of hobbies and interests in addition to his medical work. All his colleagues and friends mourn his passing.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.