Paper Info
Title
Separating quantum communication and approximate rank.
Abstract
One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially equivalent to the approximate gamma(2) norm and generalized discrepancy, and subsumes several other lower bounds. All known lower bounds on quantum communication complexity in the general unbounded-round model can be shown via the logarithm of approximate rank, and it was an open problem to give any separation at all between quantum communication complexity and the logarithm of the approximate rank. In this work we provide the first such separation: We exhibit a total function H with quantum communication complexity almost quadratically larger than the logarithm of its approximate rank. We construct H using the communication lookup function framework of Anshu et al. (FOCS 2016) based on the cheat sheet framework of Aaronson et al. (STOC 2016). From a starting function F, this framework defines a new function H = F-G. Our main technical result is a lower bound on the quantum communication complexity of F-G in terms of the discrepancy of F, which we do via quantum information theoretic arguments. We show the upper bound on the approximate rank of F-G by relating it to the Boolean circuit size of the starting function F.
Year
DOI
Venue
2017
10.4230/LIPIcs.CCC.2017.24
Leibniz International Proceedings in Informatics
Keywords
DocType
Volume
Communication Complexity,Quantum Computing,Lower Bounds,logrank,Quantum Information
Conference
79
ISSN
Citations 
PageRank 
1868-8969
0
0.34
References 
Authors
0
6
Name
Order
Citations
PageRank
Anurag Anshu14314.24
Shalev Ben-David2638.92
Ankit Garg312516.19
Rahul Jain478471.51
Robin Kothari519621.05
Troy Lee627628.96