Entanglement and coherence in quantum state merging

Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging where two parties aim to merge their parts of a tripartite quantum state. In standard quantum state merging, entanglement is considered as an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process, and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum, and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.Comment: 9 pages, 1 figure. Lemma 5 in Appendix D of the previous version was not correct. This did not affect the results of the main tex

Field Induced Magnetic Ordering and Single-ion Anisotropy in the Quasi-1D Haldane Chain Compound SrNi2V2O8: A Single Crystal investigation

Field-induced magnetic ordering in the Haldane chain compound SrNi$_{2}$V$_{2}$O$_{8}$ and effect of anisotropy have been investigated using single crystals. Static susceptibility, inelastic neutron scattering, high-field magnetization, and low temperature heat-capacity studies confirm a non-magnetic spin-singlet ground state and a gap between the singlet ground state and triplet excited states. The intra-chain exchange interaction is estimated to be $J \sim 8.9{\pm}$0.1 meV. Splitting of the dispersions into two modes with minimum energies 1.57 and 2.58 meV confirms the existence of single-ion anisotropy $D(S^z){^2}$. The value of {\it D} is estimated to be $-0.51{\pm}0.01$ meV and the easy axis is found to be along the crystallographic {\it c}-axis. Field-induced magnetic ordering has been found with two critical fields [$\mu_0H_c^{\perp c} = 12.0{\pm}$0.2 T and $\mu_0H_c^{\parallel c} = 20.8{\pm}$0.5 T at 4.2 K]. Field-induced three-dimensional magnetic ordering above the critical fields is evident from the heat-capacity, susceptibility, and high-field magnetization study. The Phase diagram in the {\it H-T} plane has been obtained from the high-field magnetization. The observed results are discussed in the light of theoretical predictions as well as earlier experimental reports on Haldane chain compounds

Spinon Confinement in the One-Dimensional Ising-Like Antiferromagnet SrCo2V2O8

For quasi-one dimensional quantum spin systems theory predicts the occurrence of a confinement of spinon excitation due to interchain couplings. Here we investigate the system SrCo2V2O8, a realization of the weakly-coupled Ising-like XXZ antiferromagnetic chains, by terahertz spectroscopy with and without applied magnetic field. At low temperatures a series of excitations is observed, which split in a Zeeman-like fashion in an applied magnetic field. These magnetic excitations are identified as the theoretically predicted spinon-pair excitations. Using a one dimensional Schr\"odinger equation with a linear confinement potential imposed by weak interchain couplings, the hierarchy of the confined spinons can be fully described.Comment: 4 pages, 3 figure

Investigation of the magnetic structure and crystal field states of pyrochlore antiferromagnet Nd2Zr2O7

We present synchrotron x-ray diffraction, neutron powder diffraction and time-of-flight inelastic neutron scattering measurements on the rare earth pyrochlore oxide Nd2Zr2O7 to study the ordered state magnetic structure and cystal field states. The structural characterization by high-resolution synchrotron x-ray diffraction confirms that the pyrochlore structure has no detectable O vacancies or Nd/Zr site mixing. The neutron diffraction reveals long range all-in/all-out antiferromagnetic order below T_N ~ 0.4 K with propagation vector k = (0 0 0) and an ordered moment of 1.26(2) \mu_B/Nd at 0.1 K. The ordered moment is much smaller than the estimated moment of 2.65 \mu_B/Nd for the local Ising ground state of Nd3+ (J=9/2) suggesting that the ordering is partially suppressed by quantum fluctuations. The strong Ising anisotropy is further confirmed by the inelastic neutron scattering data which reveals a well-isolated dipolar-octupolar type Kramers doublet ground state. The crystal field level scheme and ground state wavefunction have been determined.Comment: 12 pages, 15 figures, 2 table

Consequences of critical interchain couplings and anisotropy on a Haldane chain

Effects of interchain couplings and anisotropy on a Haldane chain have been investigated by single crystal inelastic neutron scattering and density functional theory (DFT) calculations on the model compound SrNi$_2$V$_2$O$_8$. Significant effects on low energy excitation spectra are found where the Haldane gap ($\Delta_0 \approx 0.41J$; where $J$ is the intrachain exchange interaction) is replaced by three energy minima at different antiferromagnetic zone centers due to the complex interchain couplings. Further, the triplet states are split into two branches by single-ion anisotropy. Quantitative information on the intrachain and interchain interactions as well as on the single-ion anisotropy are obtained from the analyses of the neutron scattering spectra by the random phase approximation (RPA) method. The presence of multiple competing interchain interactions is found from the analysis of the experimental spectra and is also confirmed by the DFT calculations. The interchain interactions are two orders of magnitude weaker than the nearest-neighbour intrachain interaction $J$ = 8.7~meV. The DFT calculations reveal that the dominant intrachain nearest-neighbor interaction occurs via nontrivial extended superexchange pathways Ni--O--V--O--Ni involving the empty $d$ orbital of V ions. The present single crystal study also allows us to correctly position SrNi$_2$V$_2$O$_8$ in the theoretical $D$-$J_{\perp}$ phase diagram [T. Sakai and M. Takahashi, Phys. Rev. B 42, 4537 (1990)] showing where it lies within the spin-liquid phase.Comment: 12 pages, 12 figures, 3 tables PRB (accepted). in Phys. Rev. B (2015

Learning from the early adopters: developing the digital practitioner

This paper explores how Sharpe and Beetham’s Digital Literacies Framework which was derived to model students’ digital literacies, can be applied to lecturers’ digital literacy practices. Data from a small-scale phenomenological study of higher education lecturers who used Web 2.0 in their teaching and learning practices are used to examine if this pyramid model represents their motivations for adopting technology-enhanced learning in their pedagogic practices. The paper argues that whilst Sharpe and Beetham’s model has utility in many regards, these lecturers were mainly motivated by the desire to achieve their pedagogic goals rather than by a desire to become a digital practitioner