Random coding exponents galore via decoupling
arXiv:1504.07075
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 Rényi α-information-theoretic quantity for any α (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.
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'
References in corpus (6)
- On the quantum, classical and total amount of correlations in a quantum state
- The mother of all protocols: Restructuring quantum information's family tree
- Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
- The decoupling approach to quantum information theory
- Relating different quantum generalizations of the conditional Renyi entropy
- Quantum state redistribution based on a generalized decoupling