Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A direct sum theorem in communication complexity via message compression   We prove lower bounds for the direct sum problem for two-party bounded error
randomised multiple-round communication protocols. Our proofs use the notion of
information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao
and refined further by Bar-Yossef, Jayram, Kumar and Sivakumar. Our main
technical result is a `compression' theorem saying that, for any probability
distribution $\mu$ over the inputs, a $k$-round private coin bounded error
protocol for a function $f$ with information cost $c$ can be converted into a
$k$-round deterministic protocol for $f$ with bounded distributional error and
communication cost $O(kc)$. We prove this result using a substate theorem about
relative entropy and a rejection sampling argument. Our direct sum result
follows from this `compression' result via elementary information theoretic
arguments.
  We also consider the direct sum problem in quantum communication. Using a
probabilistic argument, we show that messages cannot be compressed in this
manner even if they carry small information. Hence, new techniques may be
necessary to tackle the direct sum problem in quantum communication.

4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol