Echo-Conditioned Beamforming: A Hybrid Quantum–Probabilistic–Classical Primitive for Low-Power, Temporally and Spatially Gated Quantum Sensing

Preprint — November 2025 Echo-conditioned beamforming uses a Hahn-type quantum echo to create a deterministic temporal aperture at t = 2τ, a probabilistic mid-loop to stabilize timing/phase under drift, and a classical THz reconfigurable intelligent surface (RIS) to impose spatial directivity. The dynamics are formulated with a Lindblad open-quantum-system model and reduced to a 1D semiclassical transport picture that exposes the echo timing. A signal-to-noise inequality compares echo-assisted coupling to a RIS-only baseline. With 2024/2025 parameters a single echo-capable line is insufficient; aggregation (M ∼ 10²–10³) satisfies typical SNR margins. Instantaneous coherent power lies in the nW–µW range. Applications include quantum-enhanced NMR, directional sensing, low-probability-of-intercept THz links, and timed low-disturbance diagnostics. Code and data availability: Python/RK transport scripts and minimal QuTiP notebook (repository DOI to be supplied upon arXiv acceptance). Keywords: quantum sensing, Hahn echo, beamforming, THz metasurface, RIS, open quantum systems, Lindblad