Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A tight lower bound on the classical communication cost of entanglement
  dilution   Entanglement concentration requires no classical communication, but the best
prior art result for diluting to N copies of a partially entangled state
requires an amount of communication on the order of sqrt(N) bits. Our main
result is to prove this prior art result optimal up to a constant factor; any
procedure for creating N partially entangled states from singlets requires
Omega(sqrt(N)) bits of classical communication. Previously not even a constant
bound was known for approximate entanglement transforms.
  We also prove a lower bound on the inefficiency of the process: to dilute
singlets to N copies of a partially entangled state, the entropy of
entanglement must decrease by Omega(sqrt(N)).

2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin