Detection of Entangled States Supported by Reinforcement Learning

Discrimination of entangled states is an important element of quantum-enhanced metrology. This typically requires low-noise detection technology. Such a challenge can be circumvented by introducing nonlinear readout process. Traditionally, this is realized by reversing the very dynamics that generates the entangled state, which requires a full control over the system evolution. In this Letter, we present nonlinear readout of highly entangled states by employing reinforcement learning to manipulate the spin-mixing dynamics in a spin-1 atomic condensate. The reinforcement learning found results in driving the system toward an unstable fixed point, whereby the (to be sensed) phase perturbation is amplified by the subsequent spin-mixing dynamics. Working with a condensate of 10 900 ^{87}Rb atoms, we achieve a metrological gain of 6.97_{-1.38}^{+1.30}  dB beyond the classical precision limit. Our work will open up new possibilities in unlocking the full potential of entanglement caused quantum enhancement in experiments.