Classification of qubit entanglement: SL(2,C) versus SU(2) invariance

The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I_5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL^3 orbit of states with equal tangles but continuously varying I_5 must exist. This means that I_5 provides no information on the entanglement in the system in addition to that contained in the tangles (concurrences and threetangle) themselves. Together with the numerical evidence that I_5 is an entanglement monotone this implies that SU(2) invariance or the monotone property are too weak requirements for the characterization and quantification of entanglement for systems of three qubits, and that SL(2,C) invariance is required. This conclusion can be extended to general multipartite systems (including higher local dimension) because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex

Three-qubit entangled embeddings of CPT and Dirac groups within E8 Weyl group

In quantum information context, the groups generated by Pauli spin matrices, and Dirac gamma matrices, are known as the single qubit Pauli group P, and two-qubit Pauli group P2, respectively. It has been found [M. Socolovsky, Int. J. Theor. Phys. 43, 1941 (2004)] that the CPT group of the Dirac equation is isomorphic to P. One introduces a two-qubit entangling orthogonal matrix S basically related to the CPT symmetry. With the aid of the two-qubit swap gate, the S matrix allows the generation of the three-qubit real Clifford group and, with the aid of the Toffoli gate, the Weyl group W(E8) is generated (M. Planat, Preprint 0904.3691). In this paper, one derives three-qubit entangling groups ? P and ? P2, isomorphic to the CPT group P and to the Dirac group P2, that are embedded into W(E8). One discovers a new class of pure theequbit quantum states with no-vanishing concurrence and three-tangle that we name CPT states. States of the GHZ and CPT families, and also chain-type states, encode the new representation of the Dirac group and its CPT subgroup.Comment: 12 page

Rescaling multipartite entanglement measures for mixed states

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.Comment: Published version plus one important reference (Ref. [39]

Electron shuttle-mediated microbial Fe(III) reduction under alkaline conditions

Purpose: Extracellular Fe(III) reduction plays an important role in a variety of biogeochemical processes. Several mechanisms for microbial Fe(III) reduction in pH-neutral environments have been proposed, but pathways of microbial Fe(III) reduction within alkaline conditions have not been clearly identified. Alkaline soils are vastly distributed; thus, a better understanding of microbial Fe(III) reduction under alkaline conditions is of significance. The purpose of this study is to explore the dominant mechanism of bacterial iron reduction in alkaline environments. Materials and methods: We used antraquinone-2,6-disulfonate (AQDS) as a representative of quinone moities of humic substances and elemental sulfur and sulfate as sulfur species to investigate the potential role of humic substances and sulfur species in mediating microbial Fe(III) reduction in alkaline environments. We carried out thermodynamic calculations to predict the ability of bacteria to reduce Fe(III) (oxyhydr)oxides under alkaline conditions and the ability of AQDS and sulfur species to serve as electron acceptors for microbial anaerobic respiration in an assumed alkaline soil environments. A series of incubation experiments with two model dissimilatory metal reducing bacteria, Shewanella oneidensis MR-1 and Geobacter sulfurreducens PCA as well as mixed bacteria enriched from a soil were performed to confirm the contribution of AQDS and sulfur species to Fe(III) reduction under alkaline conditions. Results and discussion: Based on thermodynamic calculations, we predicted that, under alkaline conditions, the enzymatic reduction of Fe(III) (oxyhydr)oxides would be thermodynamically feasible but very weak. In our incubation experiments, the reduction of ferrihydrite by anaerobic cultures of Shewanella oneidensis MR-1, Geobacter sulfurreducens PCA or microbes enriched from a soil was significantly increased in the presence of S0 or AQDS. Notably, AQDS contributed more to promoting Fe(III) reduction as a soluble electron shuttle than S0 did under the alkaline conditions probably because of different mechanisms of microbial utilization of AQDS and S0. Conclusions: These results suggest that microbial reduction of Fe(III) (oxyhydr)oxides under alkaline conditions may proceed via a pathway mediated by electron shuttles such as AQDS and S0. Considering the high ability of electron shuttling and vast distribution of humic substances, we suggest that humic substance-mediated Fe(III) reduction may potentially be the dominant mechanism for Fe(III) reduction in alkaline environments

Holographic Entanglement Entropy in Lovelock Gravities

We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement entropy are governed by the conformal anomalies of the CFT; we verify that the holographic calculations are consistent with this property. We also compute the holographic entanglement entropy of a slab in the Gauss-Bonnet examples dual to relativistic and non-relativistic CFTs and discuss its properties. Finally, we discuss features of the entanglement entropy in the backgrounds dual to renormalization group flows between fixed points and comment on the implications for a possible c-theorem in four spacetime dimensions.Comment: harvmac, 30 pages, 1 figure, References added, typos correcte