Noiseless linear amplification in quantum target detection using Gaussian states

Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal-idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. For coherent states, the performance in such a scheme is bounded by one without amplification except for a few specific regimes which are defined