Entanglement Cost of Antisymmetric States and Additivity of Capacity of Some Quantum Channel

We study the entanglement cost of the states in the contragredient space, which consists of $(d-1)$ $d$-dimensional systems. The cost is always $\log_2 (d-1)$ ebits when the state is divided into bipartite \C^d \otimes (\C^d)^{d-2}. Combined with the arguments in \cite{Matsumoto02}, additivity of channel capacity of some quantum channels is also shown.Comment: revtex 4 pages, no figures, small changes in title and author's affiliation and some typo are correcte

Entanglement Cost of Three-Level Antisymmetric States

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.Comment: 8page

Remarks on additivity of the Holevo channel capacity and of the entanglement of formation

The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a given bipartite state. In particular, using the Stinespring dilation theorem, we give a formula for the channel capacity involving entanglement of formation. This can be used to show that additivity of the latter for some states can be inferred from the additivity of capacity for certain channels. We demonstrate this connection for a family of group--covariant channels, allowing us to calculate the entanglement cost for many states, including some where a strictly smaller upper bound on the distillable entanglement is known. This is presented in a general framework, extending recent findings of Vidal, Dur and Cirac (e-print quant-ph/0112131). In an appendix we speculate on a general relation of superadditivity of the entanglement of formation, which would imply both the general additivity of this function under tensor products and of the Holevo capacity (with or without linear cost constraints)

Effects of Rattling Phonons on the Quasiparticle Excitation and Dynamics in the Superconducting β\beta-Pyrochlore KOs2_2O6_6

Microwave penetration depth $\lambda$ and surface resistance at 27 GHz are measured in high quality crystals of KOs$_2$O$_6$. Firm evidence for fully-gapped superconductivity is provided from $\lambda(T)$. Below the second transition at $T_{\rm p}\sim 8$ K, the superfluid density shows a step-like change with a suppression of effective critical temperature $T_{\rm c}$. Concurrently, the extracted quasiparticle scattering time shows a steep enhancement, indicating a strong coupling between the anomalous rattling motion of K ions and quasiparticles. The results imply that the rattling phonons help to enhance superconductivity, and that K sites freeze to an ordered state with long quasiparticle mean free path below $T_{\rm p}$.Comment: 5 pages, 5 figures, to be published in Phys. Rev. Let