Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective

Abstract

We point out a contrasting role the entanglement plays in communication and estimation scenarios. In the first case it brings noticeable benefits at the measurement stage (output super-additivity), whereas in the latter it is the entanglement of the input probes that enables significant performance enhancement (input super-additivity). We identify a weak estimation regime where a strong connection between concepts crucial to the two fields is demonstrated; the accessible information and the Holevo quantity on one side and the quantum Fisher information related quantities on the other. This allows us to shed new light on the problem of super-additivity in communication using the concepts of quantum estimation theory.

31 pages, 3 figures, published version

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• Mutual Information Bounded by Fisher Information
• Low-cost limit of classical communication with restricted quantum measurements
• Two-particle indistinguishability and identification of boson-and-fermion species: a Fisher information approach