PT Journal AU Baamara, Y Gessner, M Sinatra, A TI Quantum-enhanced multiparameter estimation and compressed sensing of a field SO Scipost Physics JI SciPost Phys. PY 2023 BP 050 EP 18pp VL 14 IS 3 DI 10.21468/SciPostPhys.14.3.050 LA English AB We show that a significant quantum gain corresponding to squeezed or over-squeezed spin states can be obtained in multiparameter estimation by measuring the Hadamard coefficients of a 1D or 2D signal. The physical platform we consider consists of twolevel atoms in an optical lattice in a squeezed-Mott configuration, or more generally by correlated spins distributed in spatially separated modes. Our protocol requires the possibility to locally flip the spins, but relies on collective measurements. We give examples of applications to scalar or vector field mapping and compressed sensing. ER