# The maximum advantage of quantum illumination

## TL;DR

This paper analyzes quantum illumination as a quantum channel discrimination protocol, showing that the greatest advantage over classical methods is achieved with Bell states, using a Hilbert-Schmidt inner product measure.

## Contribution

It introduces a new approach to evaluate quantum illumination's advantage without requiring full state diagonalization, highlighting Bell states as optimal.

## Key findings

- Bell states provide maximum quantum advantage in illumination.
- Hilbert-Schmidt inner product effectively measures distinguishability.
- Quantum illumination surpasses classical methods with optimal states.

## Abstract

Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another. Computing the error probability directly requires complete knowledge and diagonalization of the density matrices describing these states. Both of these fundamental requirements become impractically difficult to obtain as the dimension of the states grow large. In this article, we analyze quantum illumination as a quantum channel discrimination protocol and circumvent these issues by using the normalized Hilbert-Schmidt inner product as a measure of distinguishability. Using this measure, we show that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state.