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DOI: 10.4230/LIPIcs.STACS.2013.424
URN: urn:nbn:de:0030-drops-39539
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3953/
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Klauck, Hartmut ; de Wolf, Ronald

Fooling One-Sided Quantum Protocols

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Abstract

We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f : X x Y -> {0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its one-sided-error quantum communication complexity with prior entanglement, and NQ(f) its nondeterministic quantum communication complexity (without prior entanglement; this model is trivial with shared randomness or entanglement). Our main results are the following, where logs are to base 2:

- If the maximal fooling set is "upper triangular" (which is for instance the case for the equality, disjointness, and greater-than functions), then we have Q_1^*(f) >= 1/2 log fool^1(f) - 1/2, which (by superdense coding) is essentially optimal for functions like equality, disjointness, and greater-than. No super-constant lower bound for equality seems to follow from earlier techniques.

- For all f we have Q_1^*(f) >= 1/4 log fool^1(f) - 1/2.

- NQ(f) >= 1/2 log fool^1(f) + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f) \approx 0.613 log fool^1(f).

BibTeX - Entry

@InProceedings{klauck_et_al:LIPIcs:2013:3953,
  author =	{Hartmut Klauck and Ronald de Wolf},
  title =	{{Fooling One-Sided Quantum Protocols}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{424--433},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3953},
  URN =		{urn:nbn:de:0030-drops-39539},
  doi =		{10.4230/LIPIcs.STACS.2013.424},
  annote =	{Keywords: Quantum computing, communication complexity, fooling set, lower bound}
}

Keywords: Quantum computing, communication complexity, fooling set, lower bound
Collection: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 26.02.2013

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