Communication over Quantum Channels with Parameter Estimation

TL;DR

This paper investigates the capacity of quantum channels with parameter estimation requirements, considering various types of channel side information, and provides new formulas and characterizations for different channel classes.

Contribution

It introduces regularized capacity-distortion formulas for quantum channels with parameter estimation, including single-letter characterizations for measurement and entanglement-breaking channels.

Findings

Derived regularized formulas for capacity-distortion regions.

Single-letter characterizations for measurement channels with causal CSI.

Extended capacity formulas to entanglement-breaking channels without CSI.

Abstract

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model can be viewed as a form of quantum metrology, and as the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche et al. (2016) on classical-quantum channels.