Moderate Deviation Expansion for Fully Quantum Tasks

IEEE Transactions on Information Theory, vol. 69, pp. 5041–5059

Abstract

The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like quantity and the error vanishes at the same time. We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks, including quantum source coding, quantum state splitting, entanglement-assisted quantum channel coding, and entanglement-assisted quantum channel simulation. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy. This allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime.

Authors 3

1. Navneeth Ramakrishnan

   Imperial College London

   Affiliation as printed

   Department of Computing, Imperial College London, London, U.K

2. Marco Tomamichel

   National University of Singapore · Centre for Quantum Technologies

   Affiliation as printed

   Department of Electrical and Computer Engineering, Centre for Quantum Technologies, National University of Singapore, Queenstown, Singapore

3. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany