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This all started because we were trying to figure out how to compress quantum data *adaptively*  i.e., without a priori knowing the source. This seems hard, because in quantum info processing, you have one hand tied behind your back. Specifically, the "Actually look at what you're doing" hand  because that would collapse the data! Anyway, we solved the problem. Our algorithm compresses quantum data, concentrates quantum entanglement, and makes coffee. But *how* it works is arguably more interesting, because at its heart is a novel and somewhat strange transformation that we called "The Streaming Elias Transform", which separates an i.i.d. stream of bits into (i) perfectly predictable bits, and (ii) perfectly random (unknown) bits, using insanely low memory [log(N)]. I'll introduce the problem (5 minutes), explain the streaming Elias transform in (20 minutes), and try desperately to put it in context (5 minutes). It's all nicely written up in Host: Peter Loxley, loxley@lanl.gov 