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Unbounded-Error Classical and Quantum Communication Complexity | | Kazuo Iwama
; Harumichi Nishimura
; Rudy Raymond
; Shigeru Yamashita
; | | Date: |
18 Sep 2007 | | Abstract: | Since the seminal work of Paturi and Simon cite[FOCS’84 & JCSS’86]{PS86},
the unbounded-error classical communication complexity of a Boolean function
has been studied based on the arrangement of points and hyperplanes. Recently,
cite[ICALP’07]{INRY07} found that the unbounded-error {em quantum}
communication complexity in the {em one-way communication} model can also be
investigated using the arrangement, and showed that it is exactly (without a
difference of even one qubit) half of the classical one-way communication
complexity. In this paper, we extend the arrangement argument to the {em
two-way} and {em simultaneous message passing} (SMP) models. As a result, we
show similarly tight bounds of the unbounded-error two-way/one-way/SMP
quantum/classical communication complexities for {em any} partial/total
Boolean function, implying that all of them are equivalent up to a
multiplicative constant of four. Moreover, the arrangement argument is also
used to show that the gap between {em weakly} unbounded-error quantum and
classical communication complexities is at most a factor of three. | | Source: | arXiv, 0709.2761 | | Services: | Forum | Review | PDF | Favorites | |
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