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A tight lower bound on the classical communication cost of entanglement dilution

Aram Harrow·Hoi-Kwong Lo
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Abstract

Entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of sqrt(N) bits. Our main result is to prove this prior art result optimal up to a constant factor; any procedure for creating N partially entangled states from singlets requires Omega(sqrt(N)) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transforms. We also prove a lower bound on the inefficiency of the process: to dilute singlets to N copies of a partially entangled state, the entropy of entanglement must decrease by Omega(sqrt(N)).

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Aram Harrow, Hoi-Kwong Lo. 2002-06-28. A tight lower bound on the classical communication cost of entanglement dilution. https://arxiv.org/abs/quant-ph/0204096

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