License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2021.30
URN: urn:nbn:de:0030-drops-143042
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14304/
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Anshu, Anurag ; Ben-David, Shalev ; Kundu, Srijita

On Query-To-Communication Lifting for Adversary Bounds

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LIPIcs-CCC-2021-30.pdf (0.9 MB)

Abstract

We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows:
1) We show that the classical adversary bound lifts to a lower bound on randomized communication complexity with a constant-sized gadget. We also show that the classical adversary bound is a strictly stronger lower bound technique than the previously-lifted measure known as critical block sensitivity, making our lifting theorem one of the strongest lifting theorems for randomized communication complexity using a constant-sized gadget.
2) Turning to quantum models, we show a connection between lifting theorems for quantum adversary bounds and secure 2-party quantum computation in a certain "honest-but-curious" model. Under the assumption that such secure 2-party computation is impossible, we show that a simplified version of the positive-weight adversary bound lifts to a quantum communication lower bound using a constant-sized gadget. We also give an unconditional lifting theorem which lower bounds bounded-round quantum communication protocols.
3) Finally, we give some new results in query complexity. We show that the classical adversary and the positive-weight quantum adversary are quadratically related. We also show that the positive-weight quantum adversary is never larger than the square of the approximate degree. Both relations hold even for partial functions.

BibTeX - Entry

@InProceedings{anshu_et_al:LIPIcs.CCC.2021.30,
  author =	{Anshu, Anurag and Ben-David, Shalev and Kundu, Srijita},
  title =	{{On Query-To-Communication Lifting for Adversary Bounds}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{30:1--30:39},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14304},
  URN =		{urn:nbn:de:0030-drops-143042},
  doi =		{10.4230/LIPIcs.CCC.2021.30},
  annote =	{Keywords: Quantum computing, query complexity, communication complexity, lifting theorems, adversary method}
}

Keywords: Quantum computing, query complexity, communication complexity, lifting theorems, adversary method
Collection: 36th Computational Complexity Conference (CCC 2021)
Issue Date: 2021
Date of publication: 08.07.2021

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