Real-time adaptive Bayesian Estimation demonstrated on a non-single-shot readout sensor*

Quantum phase-estimation algorithms enhance the sensitivity and dynamic range of sensing protocols. Adaptive Bayesian Estimation (ABE) is one example of a method that has been proven to enhance single-shot readout (SSR) sensors.  Nevertheless, many sensors do not always have an SSR capability and require averaged readout, where a threshold can be used to determine a binary result according to the number of positive measurements. This outcome is used in the likelihood function of the subsequent Bayesian update. Another approach considers the number of positive results from R measurements and uses a binomial distribution, that yields a different value for each outcome. The latter approach increases the amount of information provided.

To date, no real-time ABE with binomial distribution has been demonstrated. Here, we do this using an NV center in diamond under ambient conditions to estimate DC magnetic fields. For the adaptive part, we estimate the next sensing phase from the maximal Fisher information of the likelihood function. Demonstrating the superiority of real-time ABE with binomial distribution will be the first step towards applying enhanced quantum sensing in other non-SSR sensors, e.g., SC qubits, and for a large range of sensing methods, e.g., dynamical decoupling.