Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unbounded-Error Classical and Quantum Communication Complexity   Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86},
the unbounded-error classical communication complexity of a Boolean function
has been studied based on the arrangement of points and hyperplanes. Recently,
\cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum}
communication complexity in the {\em one-way communication} model can also be
investigated using the arrangement, and showed that it is exactly (without a
difference of even one qubit) half of the classical one-way communication
complexity. In this paper, we extend the arrangement argument to the {\em
two-way} and {\em simultaneous message passing} (SMP) models. As a result, we
show similarly tight bounds of the unbounded-error two-way/one-way/SMP
quantum/classical communication complexities for {\em any} partial/total
Boolean function, implying that all of them are equivalent up to a
multiplicative constant of four. Moreover, the arrangement argument is also
used to show that the gap between {\em weakly} unbounded-error quantum and
classical communication complexities is at most a factor of three.

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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat