Quantum Noise Fraction and the Thermal Frontier in High-Frequency Gravitational Wave Detection

We introduce a diagnostic – the quantum noise fraction $\beta$ – that determines the maximum sensitivity improvement achievable through quantum enhancement for any gravitational wave detector. Applied to the landscape of proposed high-frequency (kHz-GHz) detectors, this diagnostic reveals that resonant mass detectors operating through tidal coupling are thermally dominated ($\beta \approx 0$) at all frequencies below ~230 MHz at dilution temperatures, rendering squeezing and entanglement limited in effectiveness. Only above this thermal frontier, defined by $\mathrm{\hslash }\omega =k_{B}T\ln 3$, does the quantum regime become accessible. We identify a single concrete realization: a bulk acoustic wave resonator at 1 GHz and 10 mK ($\beta =0.98$), and propose a gravitational wave detector employing squeezed phononic states via circuit QED readout. An array of ${10}^4$ such resonators with 10 dB mechanical squeezing reaches $\sqrt{S_h}=2.1\times {10}^{-22}\mathrm{/}\sqrt{\mathrm{H}\mathrm{z}}$ – still a factor ~${10}^{12}$ above the BBN bound on stochastic backgrounds at 1 GHz, indicating that the sensitivity gap remains predominantly classical in origin and that concurrent advances in classical detector parameters will be required.