Entanglement spread and clean resource inequalities
arXiv:0909.1557 · doi:10.1142/9789814304634_0046
Abstract
This article will examine states that superpose different amounts of entanglement and protocols that run in superposition but generate or consume different amounts of entanglement. In both cases we find a uniquely quantum difficulty: entanglement cannot be conditionally discarded without either using communication or causing decoherence. I will first describe the problem of entanglement spread in states and operations, as well as some methods of dealing with it. Then I'll describe three applications to problems that at first glance appear to be quite different: first, a reinterpretation of the old observation that creating n partially entangled states from singlets requires theta(sqrt(n)) communication, but cannot itself be used to communicate; second, a new lower bound technique for communication complexity; third, an explanation of how to extend the quantum reverse Shannon theorem from tensor power sources to general sources.
11 pages. This is an extended version of an article that appeared in the proceedings of ICMP09: the 16th International Congress on Mathematical Physics. v2. Fixed a sign error in one definition