Approaches for approximate additivity of the Holevo information of quantum channels
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2018-01-25 |
| Journal | Physical review. A/Physical review, A |
| Authors | Felix Leditzky, Eneet Kaur, Nilanjana Datta, Mark M. Wilde |
| Institutions | Joint Institute for Laboratory Astrophysics, University of Cambridge |
| Citations | 108 |
Abstract
Section titled āAbstractāWe study quantum channels that are close to another channel with weakly\nadditive Holevo information and derive upper bounds on their classical\ncapacity. Examples of channels with weakly additive Holevo information are\nentanglement-breaking channels, unital qubit channels, and Hadamard channels.\nRelated to the method of approximate degradability, we define approximation\nparameters for each class above that measure how close an arbitrary channel is\nto satisfying the respective property. This gives us upper bounds on the\nclassical capacity in terms of functions of the approximation parameters, as\nwell as an outer bound on the dynamic capacity region of a quantum channel.\nSince these parameters are defined in terms of the diamond distance, the upper\nbounds can be computed efficiently using semidefinite programming (SDP). We\nexhibit the usefulness of our method with two example channels: a convex\nmixture of amplitude damping and depolarizing noise, and a composition of\namplitude damping and dephasing noise. For both channels, our bounds perform\nwell in certain regimes of the noise parameters in comparison to a recently\nderived SDP upper bound on the classical capacity. Along the way, we define the\nnotion of a generalized channel divergence (which includes the diamond distance\nas an example), and we prove that for jointly covariant channels these\nquantities are maximized by purifications of a state invariant under the\ncovariance group. This latter result may be of independent interest.\n
Tech Support
Section titled āTech SupportāOriginal Source
Section titled āOriginal SourceāReferences
Section titled āReferencesā- 2006 - XIVth International Congress on Mathematical Physics