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# Exponential Separation between Quantum Communication and Logarithm of Approximate Rank

#### Wed, Sep 11, 2019 12:30 CEST

###### Speakers:Makrand Sinha

Chattopadhyay, Mande and Sherif (to appear in STOC 2019) recently exhibited a total Boolean function, the sink function, that has polynomial approximate rank and polynomial randomized communication complexity. This gives an exponential separation between randomized communication complexity and logarithm of the approximate rank, refuting the log-approximate-rank conjecture. We show that even the quantum communication complexity of the sink function is polynomial, thus also refuting the quantum log-approximate-rank conjecture.

Our lower bound is based on the fooling distribution method introduced by Rao and Sinha (Theory of Computing 2018) for the classical case and extended by Anshu, Touchette, Yao and Yu (STOC 2017) for the quantum case. We also give a new proof of the classical lower bound using the fooling distribution method.

Joint work with Ronald de Wolf.