2014/09/30 by Mario Berta, Matthias Christandl, Dave Touchette · 4 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Conditional entropy #Converse #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum capacity #Quantum channel #Quantum entanglement #Quantum relative entropy #Quantum state #Quantum system #Upper and lower bounds #Wireless Communication Security Techniques #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1109/tit.2016.2516006
published as IEEE Trans. Info. Theo. 62, 1425 (2016) · v3: 29 pages, 1 figure, extended strong converse discussion
arxiv created 2015/09/16 · openalex publication_date 2016/01/08 · arxiv updated 2016/03/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 minand 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.