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

• URL: http://arxiv.org/abs/2602.14420v1
• Date: Mon, 16 Feb 2026 03:08:27 GMT
• Title: The Multiparameter Frontier: Metrological Hierarchy and Robustness in Dispersive Quantum Interferometry
• Authors: Lucas Ferreira R. de Moura, Daniel Y. Akamatsu, G. D. de Moraes Neto, Norton G. de Almeida,
• Abstract summary: We present a dispersive quantum thermometry protocol for simultaneous estimation of inverse temperature.<n>We derive closed-form expressions for the quantum Fisher information matrix.<n>We validate these predictions through digital quantum circuit implementation on IBM's textttibm_torino processor.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a dispersive quantum thermometry protocol for simultaneous estimation of inverse temperature $β$ 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 $\mathcal{V}(β)$ and its derivative. The output state remains diagonal in photon-number basis, making photon counting globally optimal and saturating the multiparameter quantum Cramér-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.

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