Streaming Universal Distortion-Free Entanglement Concentration

This paper presents a streaming (sequential) protocol for universal entanglement concentration at the Shannon bound. Alice and Bob begin with N identical (but unknown) two-qubit pure states, each containing E ebits of entanglement. They each run a reversible algorithm on their qubits, and end up with Y perfect EPR pairs, where Y=NE ± O(√(N)). Our protocol is streaming, so the N input systems are fed in one at a time, and perfect EPR pairs start popping out almost immediately. It matches the optimal block protocol exactly at each stage, so the average yield after n inputs is 〈 Y〉=nE-O(logn). So, somewhat surprisingly, there is no tradeoff between yield and lag-our protocol optimizes both. In contrast, the optimal N-qubit block protocol achieves the same yield, but since no EPR pairs are produced until the entire input block is read, its lag is O(N). Finally, our algorithm runs in O(log N) space, so a lot of entanglement can be efficiently concentrated using a very small (e.g., current or near-future technology) quantum processor. Along the way, we find an optimal streaming protocol for extracting randomness from classical i.i.d. sources and a more space-efficient implementation of the Schur transform.