Entanglement Witnesses for Graph States: General Theory and Examples

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.Comment: 12 pages + appendix, 7 figure

Acetylene-ammonia-18-crown-6 (1/2/1)

The title compound, C2H2·C12H24O6·2NH3, was formed by co-crystallization of 18-crown-6 and acetylene in liquid ammonia. The 18-crown-6 molecule has threefold rotoinversion symmetry. The acteylene molecule lies on the threefold axis and the whole molecule is generated by an inversion center. The two ammonia molecules are also located on the threefold axis and are related by inversion symmetry. In the crystal, the ammonia molecules are located below and above the crown ether plane and are connected by intermolecular N-H...O hydrogen bonds. The acetylene molecules are additionally linked by weak C-H...N interactions into chains that propagate in the direction of the crystallographic c axis. The 18-crown-6 molecule [occupancy ratio 0.830 (4):0.170 (4)] is disordered and was refined using a split model

Tetraamminepalladium(II) dichloride tetraammonia solvate

The title compound, [Pd(NH3)4]Cl2·4NH3, was crystallized in liquid ammonia from the salt Pd(en)Cl2 (en is ethylenediamine) and is isotypic with [Pt(NH3)4]Cl2·4NH3 [Grassl & Korber (2014). Acta Cryst. E70, i31]. The Pd2+ cation is coordinated by four ammonia molecules, exhibiting a square-planar geometry. The chloride anions are surrounded by nine ammonia molecules. These are either bound in the palladium complex or solvent molecules. The packing of the ammonia solvent molecules enables the formation of an extended network of N—H...N and N—H...Cl interactions with nearly ideal hydrogen-bonding geometry

Crystal structure of rubidium peroxide ammonia disolvate

The title compound, Rb2O2·2NH3, has been obtained as a reaction product of rubidium metal dissolved in liquid ammonia and glucuronic acid. As a result of the low-temperature crystallization, a disolvate was formed. To our knowledge, only one other solvate of an alkali metal peroxide is known: Na2O2·8H2O has been reported by Grehl et al. [Acta Cryst. (1995), C51, 1038–1040]. We determined the peroxide bond length to be 1.530 (11) Å, which is in accordance with the length reported by Bremm & Jansen [Z. Anorg. Allg. Chem. (1992), 610, 64–66]. One of the ammonia solvate molecules is disordered relative to a mirror plane, with 0.5 occupancy for the corresponding nitrogen atom

Tetraammineplatinum(II) dichloride ammonia tetrasolvate

The title compound, [Pt(NH3)4]Cl2·4NH3, was crystallized in liquid ammonia from the salt PtCl2. The platinum cation is coordinated by four ammonia molecules, forming a square-planar complex. The chloride anions are surrounded by nine ammonia molecules, either bound within the platinum complex or solvent molecules. The solvent ammonia molecules are packed in such a way that an extended network of N—H...N and N—H...Cl hydrogen bonds is formed. The structure is isotypic with [Pd(NH3)4]Cl2·4NH3 [Grassl & Korber (2014). Acta Cryst. E70, i32]

Crystal structure of rubidium methyldiazotate

The title compound, Rb+·H3CN2O−, has been crystallized in liquid ammonia as a reaction product of the reductive ammonolysis of the natural compound streptozocin. Elemental rubidium was used as reduction agent as it is soluble in liquid ammonia, forming a blue solution. Reductive bond cleavage in biogenic materials under kinetically controlled conditions offers a new approach to gain access to sustainably produced raw materials. The anion is nearly planar [dihedral angle O—N—N—C = −0.4 (2)°]. The Rb+ cation has a coordination number of seven, and coordinates to five anions. One anion is bound via both its N atoms, one by both O and N, two anions are bound by only their O atoms, and the last is bound via the N atom adjacent to the methyl group. The diazotate anions are bridged by cations and do not exhibit any direct contacts with each other. The cations form corrugated layers that propagate in the (-101) plane

Cannabidiol revisited

The crystal structure of cannabidiol, C21H30O2, {systematic name: 2-[(1R,6R)-3-methyl-6-(prop-1-en-2-yl)cyclohex-2-enyl]-5-pentylbenzene-1,3-diol}, was determined earlier by Jones et al. [(1977). Acta Cryst. B33, 3211–3214] and Ottersen & Rosenqvist [(1977). Acta Chem. Scand. B31, 749–755]. In both investigations, the absolute configuration is given as R,R, referring to Mechoulam et al. [(1967.J. Am. Chem. Soc. 89, 4552–4554]. In the latter, the absolute configuration was identified by chemical means. Using the advantages of modern single-crystal X-ray diffractometers such as area detectors and high-intensity radiation sources, a high-quality structure determination including the absolute configuration was possible and is shown in this work. Furthermore, the rather uncommon Cu Kβ wavelength radiation was applied for the structure determination, which confirmed the absolute structure to be R,R