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Smooth Entropy Bounds on One-Shot Quantum State Redistribution.
- Source :
- IEEE Transactions on Information Theory; Mar2016, Vol. 62 Issue 3, p1425-1439, 15p
- Publication Year :
- 2016
-
Abstract
- In quantum state redistribution as introduced by Luo and Devetak and Devetak and Yard, there are four systems of interest: the $A$ system held by Alice; the $B$ system held by Bob; the $C$ system that is to be transmitted from Alice to Bob; and the $R$ system that holds a purification of the state in the $ABC$ registers. We give upper and lower bounds on the amount of quantum communication and entanglement required to perform the task of quantum state redistribution in a one-shot setting. Our bounds are in terms of the smooth conditional min- and max-entropy, and the smooth max-information. The protocol for the upper bound has a clear structure, building on the work of Oppenheim: it decomposes the quantum state redistribution task into two simpler coherent state merging tasks by introducing a coherent relay. In the independent and identical (i.i.d.) asymptotic limit our bounds for the quantum communication cost converge to the quantum conditional mutual information $I(C;R|B)$ , and our bounds for the total cost converge to the conditional entropy $H(C|B)$ . This yields an alternative proof of optimality of these rates for quantum state redistribution in the i.i.d. asymptotic limit. In particular, we obtain a strong converse for quantum state redistribution, which even holds when allowing for feedback. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 62
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 113114898
- Full Text :
- https://doi.org/10.1109/TIT.2016.2516006