Optimum Mixed-State Discrimination for Noisy Entanglement-Enhanced Sensing

TLDR

Quantum metrology uses entanglement or squeezed light to surpass classical sensors, but environmental loss typically destroys these nonclassical resources; quantum illumination remains robust, offering a 6 dB advantage over coherent‑state sensors even after loss, yet an optimal receiver capable of fully exploiting this advantage has been elusive due to the need to process many noisy modes. The study demonstrates that sum‑frequency generation can be employed for optimal discrimination of multimode Gaussian‑mixed states. The authors use a sum‑frequency generation receiver, optionally augmented with feedforward, to discriminate multimode Gaussian‑mixed states. The SFG receiver saturates the quantum Chernoff bound for quantum illumination, and with feedforward it attains the Helstrom bound at low signal brightness, enabling practical quantum‑enhanced imaging, radar, tomography, and communication.

Abstract

Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources and, thus, nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise. Unfortunately, an implementation of the optimum quantum receiver that would reap QI's full performance advantage has remained elusive, owing to its having to deal with a huge number of very noisy optical modes. We show how sum-frequency generation (SFG) can be fruitfully applied to optimum multimode Gaussian-mixed-state discrimination. Applied to QI, our analysis and numerical evaluations demonstrate that our SFG receiver saturates QI's quantum Chernoff bound. Moreover, augmenting our SFG receiver with a feedforward (FF) mechanism pushes its performance to the Helstrom bound in the limit of low signal brightness. The FF-SFG receiver, thus, opens the door to optimum quantum-enhanced imaging, radar detection, state and channel tomography, and communication in practical Gaussian-state situations.