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Paper IDQ.2.1
Paper Title Second-order asymptotics of quantum data compression from partially-smoothed conditional entropy
Authors Dina Abdelhadi, EPFL, Switzerland; Joseph M. Renes, ETH Zürich, Switzerland
Session Q.2: Quantum Compression
Presentation Lecture
Track Quantum Systems, Codes, and Information
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract Anshu et al. recently introduced "partially" smoothed information measures and used them to derive tighter bounds for several information-processing tasks, including quantum state merging and privacy amplification against quantum adversaries [arXiv:1807.05630 [quant-ph]]. Yet, a tight second-order asymptotic expansion of the partially smoothed conditional min-entropy in the i.i.d. setting remains an open question. Here we establish the second-order term in the expansion for pure states, and find that it differs from that of the original "globally" smoothed conditional min-entropy. Remarkably, this reveals that the second-order term is not uniform across states, since for other classes of states the second-order term for partially and globally smoothed quantities coincides. By relating the task of quantum compression to that of quantum state merging, our derived expansion allows us to determine the second-order asymptotic expansion of the optimal rate of quantum data compression. This closes a gap in the bounds determined by Datta and Leditzky [IEEE Trans. Inf. Theory 61, 582 (2015)], and shows that the straightforward compression protocol of cutting off the eigenspace of least weight is indeed asymptotically optimal at second order.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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