Myopic Entropy Scheduling for Ramsey Magnetometry

TL;DR

The paper tackles adaptive Ramsey magnetometry by formulating an entropy-based policy to minimize posterior uncertainty about a static magnetic field $B$ through sequential measurements with tunable exposure $\tau$ and readout phase $\theta$. By framing the problem in Bayesian terms and optimizing the mutual information $I(B;X_{\tau,\theta})$, the authors show how to design measurement sequences that achieve efficient information gain and reduced measurement counts. In the idealized decoherence-free limit, the method recovers a Kitaev-like optimal schedule with an explicit iterative form $\tau_i=\tfrac{1}{2}\tau_{i-1}$ and $\theta_i=(\theta_{i-1}+\pi x_{i-1})/2$, while simulations demonstrate practical gains over baseline strategies in more realistic regimes. The work provides analytic and numerical tools, including Fourier-domain analyses, to implement entropy-based adaptive sensing and discusses extensions to imperfect readout and broader quantum sensing architectures.

Abstract

This paper presents an entropy based adaptive measurement sequence strategy for quantum sensing of magnetic fields. To physically ground our ideas we consider a sensor employing a nitrogen vacancy center in diamond, however our approach is applicable to other quantum sensor arrangements. The sensitivity and accuracy of these sensors typically rely on long sequences of rapidly occurring measurements. We introduce a new technique for designing these measurement sequences aimed at reducing the number of measurements required for a specified accuracy as measured by entropy, by selecting measurement parameters that optimally reduce entropy at each measurement. We compare, via simulation, the efficiency and sensitivity of our new method with several existing measurement sequence design strategies. Our results show quantifiable improvements in sensing performance. We also show analytically that our entropy reduction approach, reduces, under certain simplified conditions, to a well-known and widely used measurement strategy.

Figures (4)

• Figure 1: The mutual information between the measurement $X$ and magnetic field $B$, $I(X:B)$ over a Gaussian prior in $B$. All variables are quoted in natural units ($\tau', T' = \tau/\mu,\, T/\mu)$, $\theta$ is set to 0, and the standard deviation of the prior is set at $3/(\sqrt{2})$.
• Figure 2: Average decrease in entropy (top) and variance (bottom) of a variable initialised with Gaussian prior (measured in nits) over 30 measurements with parameters selected using the KPE algorithm (orange), variance reduction (green), myopic mutual information maximisation (red) and randomly (blue). $T'$ is set to 10, $\tau'$ values are capped between $0$ and $5$. Averages are obtained over 8 separate realisations with differing $B$ values.
• Figure 3: The alignment between a rescaled prior (red) with periodic components, compared against off-resonant likelihood (green), off-phase likelihood (purple) and fully decohered likelihood (blue). All three of these measurement likelihoods yield a low bias and a high measurement entropy.
• Figure 4: Bloch sphere representation for the two level model of the NV centre. Top to bottom: 1. the Bloch sphere, with unit vectors marked; 2. the rotation generated by a $\pi/2$ laser pulse (with $\theta=0$); 3. the Axis of optimal sensitivity (orange) for a given readout phase offset $\theta$, with generating rotational axis marked (red); 4. the three actions that make up a single Ramsey measurement sequence; 5. the error bands that arise from larger or smaller strength of the $\pi/2$ pulse; and 6. the error arising from blurring in $\theta$ relative phase.