# Quantum Communication Complexity of Distribution Testing

@article{Belovs2020QuantumCC, title={Quantum Communication Complexity of Distribution Testing}, author={Aleksandrs Belovs and Arturo Castellanos and Franccois Le Gall and Guillaume Malod and Alexander A. Sherstov}, journal={ArXiv}, year={2020}, volume={abs/2006.14870} }

The classical communication complexity of testing closeness of discrete distributions has recently been studied by Andoni, Malkin and Nosatzki (ICALP'19). In this problem, two players each receive $t$ samples from one distribution over $[n]$, and the goal is to decide whether their two distributions are equal, or are $\epsilon$-far apart in the $l_1$-distance. In the present paper we show that the quantum communication complexity of this problem is $\tilde{O}(n/(t\epsilon^2))$ qubits when the…

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