Exponential separation of quantum and classical one-way communication complexity
Ziv Bar-Yossef,T. S. Jayram,Iordanis Kerenidis +2 more
- pp 128-137
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TLDR
The Hidden Matching Problem HMn is defined and it is proved that any randomized linear one-way protocol with bounded error for this problem requires Ω(√[3] n log n) bits of communication.Abstract:
We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Problem HMn: Alice gets as input a string x ∈ (0, 1)n and Bob gets a perfect matching M on the n coordinates. Bob's goal is to output a tuple [i,j,b] such that the edge (i,j) belongs to the matching M and b = xi ⊕ xj. We prove that the quantum one-way communication complexity of HMn is O(log n), yet any randomized one-way protocol with bounded error must use Ω(√n) bits of communication. No asymptotic gap for one-way communication was previously known. Our bounds also hold in the model of Simultaneous Messages (SM) and hence we provide the first exponential separation between quantum SM and randomized SM with public coins.For a Boolean decision version of HMn, we show that the quantum one-way communication complexity remains O(log n) and that the 0-error randomized one-way communication complexity is Ω(n). We prove that any randomized linear one-way protocol with bounded error for this problem requires Ω(√[3] n log n) bits of communication.read more
Citations
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Journal ArticleDOI
Nonlocality and communication complexity
TL;DR: The area of quantum communication complexity is reviewed, and it is shown how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science.
Journal ArticleDOI
Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication.
TL;DR: This work presents a tripartite communication task for which such a superposition of the direction of communication allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when the authors allow for protocols with bounded error probability.
Journal ArticleDOI
Quantum Pseudo-Telepathy
TL;DR: Quantum communication complexity as mentioned in this paper uses quantum mechanics to reduce the amount of communication that would be classically required, which is an area of classical computer science that aims at quantifying the number of communication necessary to solve distributed computational problems, and is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices.
Proceedings ArticleDOI
Exponential separations for one-way quantum communication complexity, with applications to cryptography
TL;DR: In this article, an exponential separation between one-way quantum and classical communication protocols for two-partial Boolean functions was shown for two variants of the Hidden Matching Problem of Bar-Yossef et al. They used the Fourier coefficients inequality of Kahn, Kalai, and Linial.
References
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Proceedings ArticleDOI
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