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# Tutte Colloquium - Anurag Anshu

Friday, May 31, 2019 — 3:30 PM EDT

Title: Quantum Log-Approximate-Rank Conjecture is also False

 Speaker: Anurag Anshu Affiliation: Institute for Quantum Computing - University of Waterloo Room: MC 5501

Abstract:

In a recent breakthrough result, Chattopadhyay, Mande and Sherif [ECCC TR18-17] showed an exponential separation between the log approximate rank and randomized communication complexity of a total function f', hence refuting the log approximate rank conjecture of Lee and Shraibman [2009]. We provide an alternate proof of their randomized communication complexity lower bound using the information complexity approach. Using the intuition developed there, we derive a polynomially-related quantum communication complexity lower bound using the quantum information complexity approach, thus providing an exponential separation between the log approximate rank and quantum communication complexity of f'. Previously, the best known separation between these two measures was (almost) quadratic, due to Anshu, Ben-David, Garg, Jain, Kothari and Lee [CCC, 2017]. This settles one of the main question left open by Chattopadhyay, Mande and Sherif, and refutes the quantum log approximate rank conjecture of Lee and Shraibman [2009]. Along the way, we develop a Shearer-type protocol embedding for product input distributions that might be of independent interest.

Joint work with Naresh Good Boddu and Dave Touchette (https://arxiv.org/abs/1811.10525)

Location
MC - Mathematics & Computer Building
5501
200 University Avenue West

Waterloo, ON N2L 3G1

### November 2020

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