Sequential Measurements as a Resource in Ancilla-Assisted Quantum Metrology

Abstract:We present a protocol for simultaneous estimation of both quadratures of a displacement channel on a quantum harmonic oscillator using a single ancilla qubit, without complex state preparation or adaptive control. The qubit is coupled to the quantum harmonic oscillator via controlled displacements of strength $A$ and undergoes $N$ rounds of measurement and reset, while the oscillator coherently accumulates the displacement signal. The non-commuting displacements imprint an order-dependent geometric phase at each round, giving a quantum Fisher information that scales as $\mathcal{O}(A^{2} N^{3})$. Although the measurement record space grows as $2^N$, we show that exact likelihoods for any individual measurement record can be computed in $\mathcal{O}(N^{2})$ time. With this, we show that measurement in the computational basis approximately saturates the quantum bound and maintains the $\mathcal{O}(A^2 N^3)$ scaling. Furthermore, the periodic information extraction makes the protocol robust to decoherence. Our results provide a framework for the design and analysis of sequential measurement in ancilla-assisted protocols.

arXiv:2605.00287 [quant-ph]

(or arXiv:2605.00287v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.00287 Focus to learn more arXiv-issued DOI via DataCite

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