Random coding exponents galore via decoupling
Abstract
A missing piece in quantum information theory, with very few exceptions, has been to provide the random coding exponents for quantum information-processing protocols. We remedy the situation by providing these exponents for a variety of protocols including those at the top of the family tree of protocols. Our line of attack is to provide an exponential bound on the decoupling error for a restricted class of completely positive maps where a key term in the exponent is in terms of a R\'enyi \alpha-information-theoretic quantity for any \alpha (1,2]. Among the protocols covered are fully quantum Slepian-Wolf, quantum state merging, quantum state redistribution, quantum/classical communication across channels with side information at the transmitter with or without entanglement assistance, and quantum communication across broadcast channels.
Cite
@article{arxiv.1504.07075,
title = {Random coding exponents galore via decoupling},
author = {Naresh Sharma},
journal= {arXiv preprint arXiv:1504.07075},
year = {2015}
}
Comments
The changes are confined to Sec. 10. Added an exponentially decaying term to (152) ((149) in previous version) to make it precise - this makes the trace of one state to be one, this adds 1 more error term and 3 more equations, made the multiplying factor in the errors to be 20, and in few places the system labels were 'F' instead of 'G'