TY - GEN
T1 - Strong converse theorems using Rényi entropies
AU - Leditzky, Felix
AU - Wilde, Mark M.
AU - Datta, Nilanjana
N1 - Publisher Copyright:
© 2016 IEEE.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - We use a Rényi entropy method to prove a strong converse theorem for the task of quantum state redistribution. More precisely, we establish the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where the entanglement cost e and quantum communication cost q are the operational rates describing a state redistribution protocol. The strong converse property is deduced from explicit bounds on the fidelity of the protocol in terms of a Rényi generalization of the optimal rates. Hence, we identify candidates for the strong converse exponents for entanglement cost e and quantum communication cost q, respectively. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities to the fidelity of two quantum states.
AB - We use a Rényi entropy method to prove a strong converse theorem for the task of quantum state redistribution. More precisely, we establish the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where the entanglement cost e and quantum communication cost q are the operational rates describing a state redistribution protocol. The strong converse property is deduced from explicit bounds on the fidelity of the protocol in terms of a Rényi generalization of the optimal rates. Hence, we identify candidates for the strong converse exponents for entanglement cost e and quantum communication cost q, respectively. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities to the fidelity of two quantum states.
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U2 - 10.1109/ISIT.2016.7541819
DO - 10.1109/ISIT.2016.7541819
M3 - Conference contribution
AN - SCOPUS:84985930759
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2849
EP - 2853
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -