Single-Ensemble Multiparameter Squeezing with Qudits
Quantum-enhanced multiparameter sensing is often associated with distributed architectures or 2-anticoherent states, whereas squeezing in a single collective ensemble is typically limited to single-parameter metrology. Here, we show that a single ensemble can support simultaneous multiparameter squeezing when each sensor is promoted from a qubit to a qudit (i.e., spin with $d$ energy levels). We develop a general framework in which the optimal product probe state, the corresponding global readout observables, and the associated squeezing parameters are all determined from the single-site quantum Fisher information matrix. We then present a minimal qudit construction for two-parameter vector magnetic field sensing with local dimension $d=3$. We further identify a collective twisting-like interacting Hamiltonian that generates such multiparameter-squeezed states and numerically demonstrate scalable metrological gain. In particular, for a trapped-ion qutrit chain with power-law interactions, we obtain up to 12 dB enhancement in two-parameter sensing for $N=256$ sensors. Our results establish qudit-enabled multiparameter squeezing in a single ensemble as a distinct route to multiparameter quantum metrology with global readout, and highlight its potential advantage over distributed multi-ensemble strategies in the fixed-sensor-budget regime.