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.2023.25
URN: urn:nbn:de:0030-drops-182957
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18295/
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Arunachalam, Srinivasan ; Girish, Uma

Trade-Offs Between Entanglement and Communication

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LIPIcs-CCC-2023-25.pdf (0.9 MB)

Abstract

We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on n bits for which reducing the entanglement increases the classical communication complexity exponentially. Our separations are as follows. For every k ≥ ~1:
Q‖^* versus R2^*: We show that quantum simultaneous protocols with Θ̃(k⁵log³n) qubits of entanglement can exponentially outperform two-way randomized protocols with O(k) qubits of entanglement. This resolves an open problem from [Dmitry Gavinsky, 2008] and improves the state-of-the-art separations between quantum simultaneous protocols with entanglement and two-way randomized protocols without entanglement [Gavinsky, 2019; Girish et al., 2022].
R‖^* versus Q‖^*: We show that classical simultaneous protocols with Θ̃(k log n) qubits of entanglement can exponentially outperform quantum simultaneous protocols with O(k) qubits of entanglement, resolving an open question from [Gavinsky et al., 2006; Gavinsky, 2019]. The best result prior to our work was a relational separation against protocols without entanglement [Gavinsky et al., 2006].
R‖^* versus R1^*: We show that classical simultaneous protocols with Θ̃(k log n) qubits of entanglement can exponentially outperform randomized one-way protocols with O(k) qubits of entanglement. Prior to our work, only a relational separation was known [Dmitry Gavinsky, 2008].

BibTeX - Entry

@InProceedings{arunachalam_et_al:LIPIcs.CCC.2023.25,
  author =	{Arunachalam, Srinivasan and Girish, Uma},
  title =	{{Trade-Offs Between Entanglement and Communication}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{25:1--25:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18295},
  URN =		{urn:nbn:de:0030-drops-182957},
  doi =		{10.4230/LIPIcs.CCC.2023.25},
  annote =	{Keywords: quantum, communication complexity, exponential separation, boolean hidden matching, forrelation, xor lemma}
}

Keywords: quantum, communication complexity, exponential separation, boolean hidden matching, forrelation, xor lemma
Collection: 38th Computational Complexity Conference (CCC 2023)
Issue Date: 2023
Date of publication: 10.07.2023

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