Remote information concentration and multipartite entanglement in multilevel systems

Remote information concentration (RIC) in $d$-level systems (qudits) is studied. It is shown that the quantum information initially distributed in three spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. The entangled channel can be different types of genuine multipartite pure entangled states which are inequivalent under local operations and classical communication. The entangled channel can also be a mixed entangled state, even a bound entangled state which has a similar form to the Smolin state, but has different features from the Smolin state. A common feature of all these pure and mixed entangled states is found, i.e., they have $d^2$ common commuting stabilizers. The differences of qudit-RIC and qubit-RIC ($d=2$) are also analyzed.Comment: 10 pages, 3 figure

Poly[[aqua­bis(μ3-isonicotinato-κ3 O:O′:N)tris­(μ2-isonicotinato-κ3 O,O′:N)(nitrato-κO)bis­(μ4-oxalato-κ6 O 1,O 2:O 2:O 1′,O 2′:O 1′)dierbium(III)tetra­silver(I)] tetra­hydrate]

In the title coordination polymer, {[Ag4Er2(C6H4NO2)5(C2O4)2(NO3)(H2O)]·4H2O}n, each ErIII atom is coordinated in a bicapped trigonal–prismatic coordination geometry by three O atoms from two isonicotinate (IN) ligands, four O atoms from two oxalate ligands and one O atom from either a nitrate ion or a water mol­ecule, both of which are half-occupied over the same site. One AgI atom has a Y-shaped geometry defined by one N atom from one IN ligand, one O atom from another IN ligand and one O atom from an oxalate ligand. The other AgI atom is coordinated by two IN ligands and one O atom from an oxalate ligand. One of the IN ligands is disordered over an inversion center and forms a bridge between two centrosymmetric AgI ions. Due to the disorder, this IN ligand coordinates to the Ag atom through either the pyridyl N or the carboxyl­ate O atoms. The IN and oxalate ligands link the Er and Ag atoms into a three-dimensional coordination framework. O—H⋯O and C—H⋯O hydrogen bonds are observed in the crystal structure