Signal-to-noise-ratio and maximum-signal-to-noise-ratio detection statistics in template-bank searches for exotic physics transients with networks of quantum sensors

Quantum sensor networks such as the existing of atomic clocks and magnetometers offer intriguing capabilities in searches for transient signals dark matter or fields sourced by powerful astrophysical events. The common matched-filter technique relies on signal-to-noise-ratio (SNR) detection statistic to probe transients. For macroscopic objects, network would register a sweeping signal object propagates through at galactic velocities. A potential event is registered when SNR from specific template exceeds threshold set desired false positive rate. Generically, span continuous parameter space network-exotic-physics encounter, one has deal with multiple templates. In template-bank searches, natural generalization maximum-signal-to-noise-ratio (SNR-max) statistic, defined maximum absolute values SNRs determined individual matching. While realizations are Gaussian distributed, SNR-max probability distribution non-Gaussian. Moreover, computed using same data streams, become correlated between Cross-template correlations have sizable effect cumulative distributions, values. Computing large banks computationally prohibitive we develop analytic approaches computing properties statistic. This done cases bank nearly orthogonal (small cross-template correlations) correlation coefficient ``squeezed'' about most probable value. Since coefficients quantify similarity templates, increasing tend decrease thresholds rates. Increasing number templates increases thresholds. Our derivations carried out that may exhibit colored noise cross-node correlations. Specific applications illustrated search onboard satellites Global Positioning System ``toy'' planar cyclic rotational symmetry.