Gaussian Quantum Illumination via Monotone Metrics

TL;DR

This paper analyzes Gaussian quantum illumination using monotone metrics, deriving explicit formulas for decay constants, identifying optimal states, and proposing practical setups to improve target detection in noisy environments.

Contribution

It provides explicit analytic formulas for decay constants in Gaussian quantum illumination, identifies optimal probe states, and suggests practical experimental setups to enhance detection performance.

Findings

Two-mode squeezed vacuum states are optimal among pure Gaussian states.

Displacing low mean photon number TMSV states is a feasible alternative.

Efficient idler memory is crucial to outperform coherent states.

Abstract

Quantum illumination is to discern the presence or absence of a low reflectivity target, where the error probability decays exponentially in the number of copies used. When the target reflectivity is small so that it is hard to distinguish target presence or absence, the exponential decay constant falls into a class of objects called monotone metrics. We evaluate monotone metrics restricted to Gaussian states in terms of first-order moments and covariance matrix. Under the assumption of a low reflectivity target, we explicitly derive analytic formulae for decay constant of an arbitrary Gaussian input state. Especially, in the limit of large background noise and low reflectivity, there is no need of symplectic diagonalization which usually complicates the computation of decay constants. First, we show that two-mode squeezed vacuum (TMSV) states are the optimal probe among pure Gaussian states with fixed signal mean photon number. Second, as an alternative to preparing TMSV states with high mean photon number, we show that preparing a TMSV state with low mean photon number and displacing the signal mode is a more experimentally feasible setup without degrading the performance that much. Third, we show that it is of utmost importance to prepare an efficient idler memory to beat coherent states and provide analytic bounds on the idler memory transmittivity in terms of signal power, background noise, and idler memory noise. Finally, we identify the region of physically possible correlations between the signal and idler modes that can beat coherent states.