Violation of monogamy inequality for higher-dimensional objects

Bipartite quantum entanglement for qutrits and higher-dimensional objects is considered. We analyze the possibility of violation of monogamy inequality, introduced by Coffman, Kundu, and Wootters, for some systems composed of such objects. An explicit counterexample with a three-qutrit totally antisymmetric state is presented. Since three-tangle has been confirmed to be a natural measure of entanglement for qubit systems, our result shows that the three-tangle is no longer a legitimate measure of entanglement for states with three qutrits or higher dimensional objects.Comment: 2.5 pages,minor modifications are mad

Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices

By using the asymptotic theory of Pemantle and Wilson, exact asymptotic expansions of the free energy of the monomer-dimer model on rectangular $n \times \infty$ lattices in terms of dimer density are obtained for small values of $n$, at both high and low dimer density limits. In the high dimer density limit, the theoretical results confirm the dependence of the free energy on the parity of $n$, a result obtained previously by computational methods. In the low dimer density limit, the free energy on a cylinder $n \times \infty$ lattice strip has exactly the same first $n$ terms in the series expansion as that of infinite $\infty \times \infty$ lattice.Comment: 9 pages, 6 table

Geometrically asymmetric electrodes for probing electrochemical reaction kinetics: a case study of hydrogen at the Pt–CsH_2PO_4 interface

Electrochemical reactions can exhibit considerable asymmetry, with the polarization behavior of oxidation at a given metal|electrolyte interface differing substantially from that of reduction. The reference-less, microcontact electrode geometry, in which the electrode overpotentials are geometrically constrained to the working electrode (by limiting its area) is experimentally convenient, particularly for fuel cell studies, because the results do not rely on accurate placement of a reference electrode nor must oxidant and reductant gases be sealed off from one another. Here, the conditions under which the critical assumption of this geometry applies -— that the overpotential at the large-area counter electrode can be ignored -— is numerically assessed. It is found that, for cells of sufficiently large area, the effective radius of the counter electrode (which defines the area through which the majority of the current passes) can be expressed directly as a function of electrolyte thickness and the materials properties, σ, the conductivity of the electrolyte, and k, the reaction rate constant for the electrochemical reaction at zero-bias. From this effective radius and the true radius of the working electrode, the fraction of electrode overpotential at the latter, defined as the extent of isolation, can be readily computed. Experimental studies of hydrogen electro-oxidation/proton electro-reduction at the Pt|CsH_2PO_4 interface using two cells of differing dimensions both validate the computational results and demonstrate that asymmetry in such reactions are readily revealed in the micro-electrode, reference-less geometry. The study furthermore confirms the insensitivity of the results to the precise placement of the working electrode, while indicating the importance of very high isolation values (>99%) to ensure that overpotential contributions of the counter electrode do not influence the measurements, particularly as bias is increased

Bounds on Negativity of Superpositions

The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. Furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. The bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. These bounds can find useful applications in estimating the amount of the entanglement of a given pure state.Comment: 5 page

Teleporting a rotation on remote photons

Quamtum remote rotation allows implement local quantum operation on remote systems with shared entanglement. Here we report an experimental demonstration of remote rotation on single photons using linear optical element. And the local dephase is also teleported during the process. The scheme can be generalized to any controlled rotation commutes with $\sigma_{z}$.Comment: 5 pages, 4 figure

Quantum state redistribution based on a generalized decoupling

We develop a simple protocol for a one-shot version of quantum state redistribution, which is the most general two-terminal source coding problem. The protocol is simplified from a combination of protocols for the fully quantum reverse Shannon and fully quantum Slepian-Wolf problems, with its time-reversal symmetry being apparent. When the protocol is applied to the case where the redistributed states have a tensor power structure, more natural resource rates are obtained