Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct Sum Theorem for Bounded Round Quantum Communication Complexity   We prove a direct sum theorem for bounded round entanglement-assisted quantum
communication complexity. To do so, we use the fully quantum definition for
information cost and complexity that we recently introduced, and use both the
fact that information is a lower bound on the communication, and the fact that
a direct sum property holds for quantum information complexity. We then give a
protocol for compressing a single copy of a protocol down to its quantum
information cost, up to terms depending on the number of rounds and the allowed
increase in error. Two important tools to derive this protocol are a smooth
conditional min-entropy bound for a one-shot quantum state redistribution
protocol, and the quantum substate theorem of Jain, Radhakrishnan and Sen
(FOCS'02) to transform this bound into a von Neumann conditional entropy bound.
This result further establishes the newly introduced notions of quantum
information cost and complexity as the correct quantum generalisations of the
classical ones in the standard communication complexity setting. Finding such a
quantum generalization of information complexity was one of the open problem
recently raised by Braverman (STOC'12).

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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex