Inefficiency and classical communication bounds for conversion between partially entangled pure bipartite states

We derive lower limits on the inefficiency and classical communication costs of dilution between two-term bipartite pure states that are partially entangled. We first calculate explicit relations between the allowable error and classical communication costs of entanglement dilution using the protocol of Lo-Popescu and then consider a two-stage dilution from singlets with this protocol followed by some unknown protocol for conversion between partially entangled states. Applying the lower bounds on classical communication and inefficiency of Harrow-Lo and Hayden-Winter to this two-stage protocol, we derive bounds for the unknown protocol. In addition we derive analogous (but looser) bounds for general pure states.Comment: Revised version: 8 pages, 3 figures, two-column. Have added bounds for general pure states, corrected typos and updated format to PRA versio

Random bipartite entanglement from W and W-like states

We describe a protocol for distilling maximally entangled bipartite states between random pairs of parties from those sharing a tripartite W state, and show that, rather surprisingly, the total distillation rate (the total number of EPR pairs distilled per W, irrespective of who shares them) may be done at a higher rate than distillation of bipartite entanglement between specified pairs of parties. Specifically, the optimal distillation rate for specified entanglement for the W has been previously shown to be the asymptotic entanglement of assistance of 0.92 EPR pairs per W, while our protocol can asymptotically distill 1 EPR pair per W between random pairs of parties, which we conjecture to be optimal. We thus demonstrate a tradeoff between the overall asymptotic rate of EPR distillation and the distribution of final EPR pairs between parties. We further show that by increasing the number of parties in the protocol that there exist states with fixed lower-bounded distillable entanglement for random parties but arbitrarily small distillable entanglement for specified parties.Comment: 5 pages, 1 figure, RevTeX. v2 - upper bound on random distillation is expressed more generally and corollaries to the bound added. Minor notation changes. v3 - further notation changes (Ernd now designated Et), discussion of finite distillation rounds and single-copy bound on Et added. Theorem added - relative entropy is shown to be an upper bound to Et for all pure states. Discussion of W formation from EPRs (previously shown in others' work) removed. Some addition, removal and reordering of reference

Quantum secret sharing with qudit graph states

We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.Comment: 13 pages, 12 figures. v2: Corrected to reflect imperfections of (n,n) QQ protocol. Also changed notation from $(n,m)$ to $(k,n)$, corrected typos, updated references, shortened introduction. v3: Updated acknowledgement