Streaming universal distortion-free entanglement concentration

Blume-Kohout, R., Croke, S. and Gottesman, D. (2014) Streaming universal distortion-free entanglement concentration. IEEE Transactions on Information Theory, 60(1), pp. 334-350. (doi:10.1109/TIT.2013.2292135)

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Abstract

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 $Y=NE,pm, O(sqrt N)$. 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 $leftlangle Yrightrangle=nE-O(log n)$. 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Croke, Dr Sarah
Authors: Blume-Kohout, R., Croke, S., and Gottesman, D.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:IEEE Transactions on Information Theory
ISSN:0018-9448
ISSN (Online):1557-9654

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