Entanglement-Enhanced Phase Estimation without Prior Phase Information

Abstract

We study the generation of planar quantum squeezed (PQS) states by quantum nondemolition (QND) measurement of an ensemble of Rb87 atoms with a Poisson distributed atom number. Precise calibration of the QND measurement allows us to infer the conditional covariance matrix describing the Fy and Fz components of the PQS states, revealing the dual squeezing characteristic of PQS states. PQS states have been proposed for single-shot phase estimation without prior knowledge of the likely values of the phase. We show that for an arbitrary phase, the generated PQS states can give a metrological advantage of at least 3.1 dB relative to classical states. The PQS state also beats, for most phase angles, single-component-squeezed states generated by QND measurement with the same resources and atom number statistics. Using spin squeezing inequalities, we show that spin-spin entanglement is responsible for the metrological advantage.