Noam Lifshitz

We study the one-clean-qubit model of quantum communication where one qubit is in a pure state and all other qubits are maximally mixed. We demonstrate a partial function that has a quantum protocol of cost O(log N) in this model, however, every interactive randomized protocol has cost Ømega(sqrtN), settling a conjecture of Klauck and Lim. In contrast, all prior quantum versus classical communication separations required at least Ømega(log N) clean qubits. The function demonstrating our separation also has an efficient protocol in the quantum-simultaneous-with-entanglement model of cost O(log N). We thus recover the state-of-the-art separations between quantum and classical communication complexity. Our proof is based on a recent hypercontractivity inequality introduced by Ellis, Kindler, Lifshitz, and Minzer, in conjunction with tools from the representation theory of compact Lie groups.