20 research outputs found
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 to , corrected typos,
updated references, shortened introduction. v3: Updated acknowledgement