1,529 research outputs found
Assisted Entanglement Distillation
Motivated by the problem of designing quantum repeaters, we study
entanglement distillation between two parties, Alice and Bob, starting from a
mixed state and with the help of "repeater" stations. To treat the case of a
single repeater, we extend the notion of entanglement of assistance to
arbitrary mixed tripartite states and exhibit a protocol, based on a random
coding strategy, for extracting pure entanglement. The rates achievable by this
protocol formally resemble those achievable if the repeater station could merge
its state to one of Alice and Bob even when such merging is impossible. This
rate is provably better than the hashing bound for sufficiently pure tripartite
states. We also compare our assisted distillation protocol to a hierarchical
strategy consisting of entanglement distillation followed by entanglement
swapping. We demonstrate by the use of a simple example that our random
measurement strategy outperforms hierarchical distillation strategies when the
individual helper stations' states fail to individually factorize into portions
associated specifically with Alice and Bob. Finally, we use these results to
find achievable rates for the more general scenario, where many spatially
separated repeaters help two recipients distill entanglement.Comment: 25 pages, 4 figure
Unconstrained distillation capacities of a pure-loss bosonic broadcast channel
Bosonic channels are important in practice as they form a simple model for
free-space or fiber-optic communication. Here we consider a single-sender
two-receiver pure-loss bosonic broadcast channel and determine the
unconstrained capacity region for the distillation of bipartite entanglement
and secret key between the sender and each receiver, whenever they are allowed
arbitrary public classical communication. We show how the state merging
protocol leads to achievable rates in this setting, giving an inner bound on
the capacity region. We also evaluate an outer bound on the region by using the
relative entropy of entanglement and a `reduction by teleportation' technique.
The outer bounds match the inner bounds in the infinite-energy limit, thereby
establishing the unconstrained capacity region for such channels. Our result
could provide a useful benchmark for implementing a broadcasting of
entanglement and secret key through such channels. An important open question
relevant to practice is to determine the capacity region in both this setting
and the single-sender single-receiver case when there is an energy constraint
on the transmitter.Comment: v2: 6 pages, 3 figures, introduction revised, appendix added where
the result is extended to the 1-to-m pure-loss bosonic broadcast channel. v3:
minor revision, typo error correcte
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