# Optimal discrimination of optical coherent states cannot always be realized by interfering with coherent light, photon counting, and feedback

## TL;DR

This paper demonstrates that for ternary optical coherent states, the optimal minimum error measurement cannot always be implemented using traditional interference, photon counting, and feedback methods, highlighting fundamental limitations.

## Contribution

It shows that the commonly used receiver design cannot achieve the absolute minimum error for ternary states and formulates an upper bound via convex programming.

## Key findings

- Upper bound on success probability derived for ternary states
- Traditional receiver design does not reach the minimum error bound
- Numerical methods used to establish limitations of current techniques

## Abstract

It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed coherent states, this bound does not reach that of a minimum error measurement.