The structure and the magnetic properties of layered Li3Cu2SbO6 areinvestigated by powder X-ray diffraction, static susceptibility, and electronspin resonance studies up to 330 GHz. The XRD data experimentally verify thespace group C2/m with halved unit cell volume in contrast to previouslyreported C2/c. In addition, the data show significant Li/Cu-intersite exchange.Static magnetic susceptibility and ESR measurements show two magneticcontributions, i.e. quasi-free spins at low-temperature and a spin-gappedmagnetic subsystem, with about half of the spins being associated to eachsubsystem. The data suggest ferromagnetic-antiferromagnetic alternating chainswith JFM = -285 K and JAFM = 160 K with a significant amount of Li-defects inthe chains. The results are discussed in the scenario of fragmented 1D S = 1AFM chains with a rather high defect concentration of about 17% and associatedS = 1/2 edge states of the resulting finite Haldane chains.
In this paper we consider an application of the recently proposed quantumhashing technique for computing Boolean functions in the quantum communicationmodel. The combination of binary functions on non-binary quantum hash functionis done via polynomial presentation, which we have called a characteristic of aBoolean function. Based on the characteristic polynomial presentation ofBoolean functions and quantum hashing technique we present a method forcomputing Boolean functions in the quantum one-way communication model, whereone of the parties performs his computations and sends a message to the otherparty, who must output the result after his part of computations. Some of theresults are also true in a more restricted Simultaneous Message Passing modelwith no shared resources, in which communicating parties can interact only viathe referee. We give several examples of Boolean functions whose polynomialpresentations have specific properties allowing for construction of quantumcommunication protocols that are provably exponentially better than classicalones in the simultaneous message passing setting.