The minimum Renyi entropy output of a quantum channel is locally additive
arXiv:1601.00982 · doi:10.1007/s11005-016-0933-8
Abstract
We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter alpha>1. While our work extends the results of [10] (in which local additivity was proven for alpha=1), it is based on several new techniques that incorporate the multiplicative nature of p-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Renyi additivity conjectures exhibit global effects of quantum channels. Interestingly, the approach presented here can not be extended to Renyi entropies with parameter alpha<1.
15 pages, no figures, comments are welcome. Few references added. Some typos fixed. Some of the preliminaries of arXiv:1105.6122 have been reused here
References in corpus (6)
- The second laws of quantum thermodynamics
- The Quantum Chernoff Bound
- Quantum Communication With Zero-Capacity Channels
- Necessary and Sufficient Conditions for the Trumping Relation
- Catalytic Conversion Probabilities for Bipartite Pure States
- Additivity of minimal entropy output for a class of covariant channels