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.

35 pages, 11 figures, including supplemental material