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- W4387389686 abstract "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 $Omega(sqrt{N})$, settling a conjecture of Klauck and Lim. In contrast, all prior quantum versus classical communication separations required at least $Omega(log N)$ 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." @default.
- W4387389686 created "2023-10-06" @default.
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- W4387389686 date "2023-10-03" @default.
- W4387389686 modified "2023-10-07" @default.
- W4387389686 title "One Clean Qubit Suffices for Quantum Communication Advantage" @default.
- W4387389686 doi "https://doi.org/10.48550/arxiv.2310.02406" @default.
- W4387389686 hasPublicationYear "2023" @default.
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