# The capacity of coherent-state adaptive decoders with interferometry and single-mode detectors

## TL;DR

This paper investigates the limits of adaptive decoders using interferometry and single-mode detectors for coherent states, showing they cannot surpass the capacity of single-mode decoders in certain quantum channels.

## Contribution

It demonstrates that a broad class of adaptive decoders cannot outperform single-mode decoders in classical communication over quantum phase-insensitive Gaussian channels.

## Key findings

- Optimal information rate of ADs is not greater than single-mode decoders.
- Ultimate capacity of these channels is unlikely to be achieved with the considered ADs.
- Adaptive procedures based on passive multi-mode Gaussian unitaries do not improve capacity.

## Abstract

A class of Adaptive Decoders (AD's) for coherent-state sequences is studied, including in particular the most common technology for optical-signal processing, e.g., interferometers, coherent displacements and photon-counting detectors. More generally we consider AD's comprising adaptive procedures based on passive multi-mode Gaussian unitaries and arbitrary single-mode destructive measurements. For classical communication on quantum phase-insensitive Gaussian channels with a coherent-state encoding, we show that the AD's optimal information transmission rate is not greater than that of a single-mode decoder. Our result also implies that the ultimate classical capacity of quantum phase-insensitive Gaussian channels is unlikely to be achieved with the considered class of AD's.