  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.
