The Multiparameter Frontier: Metrological Hierarchy and Robustness in Dispersive Quantum Interferometry

TL;DR

This paper introduces a dispersive quantum thermometry method using a nonlinear interferometer to simultaneously estimate temperature and interaction strength, analyzing robustness and practical implementation on NISQ hardware.

Contribution

It derives a closed-form quantum Fisher information matrix for multiparameter estimation, compares robustness of different quantum states under noise, and demonstrates experimental validation on IBM quantum hardware.

Findings

Photon counting is globally optimal for the protocol.

Squeezed vacuum states are robust under loss for steady-state sensing.

Cat states are effective for transient thermometry despite photon loss.

Abstract

We present a dispersive quantum thermometry protocol for simultaneous estimation of inverse temperature $\beta$ and interaction strength $x$ using a nonlinear Mach-Zehnder interferometer coupled to a thermal ancilla. We derive closed-form expressions for the quantum Fisher information matrix, establishing that metrological performance depends solely on the thermal visibility $\mathcal{V}(\beta)$ and its derivative. The output state remains diagonal in photon-number basis, making photon counting globally optimal and saturating the multiparameter quantum Cram\'er-Rao bound without adaptive feedback. Moving beyond ideal unitary evolution, we analyze protocol robustness under concurrent amplitude and phase damping. Using Fisher Information Susceptibility, we establish a clear hierarchy: NOON states offer maximal theoretical sensitivity but exhibit exponential fragility to loss, rendering them impractical. Squeezed vacuum states emerge as robust candidates for steady-state sensing, while cat states prove compelling for transient thermometry by retaining significant coherence after photon loss. We validate these predictions through digital quantum circuit implementation on IBM's \texttt{ibm_torino} processor. Experimental results confirm the predicted Fisher information landscape while revealing systematic noise-induced biases, demonstrating that current NISQ hardware can effectively benchmark fundamental trade-offs in multiparameter quantum sensing.