Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 59, Issue 11, Pages 7693-7710Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2013.2276628
Keywords
Finite block length; information spectrum; one-shot entropies; quantum side information; randomness extraction; second-order asymptotics; source compression
Funding
- National Research Foundation
- Ministry of Education of Singapore
- MEXT [20686026]
- National Institute of Information and Communication Technology (NICT), Japan
- [23246071]
- Grants-in-Aid for Scientific Research [23246071] Funding Source: KAKEN
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We consider two fundamental tasks in quantum information theory, data compression with quantum side information, as well as randomness extraction against quantum side information. We characterize these tasks for general sources using so-called one-shot entropies. These characterizations-in contrast to earlier results-enable us to derive tight second-order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree (up to logarithmic terms) with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our technique also naturally yields bounds on operational quantities for finite block lengths.
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