# Entanglement-enhanced phase estimation without prior phase information

## TL;DR

This paper demonstrates how planar quantum squeezed states generated via quantum non-demolition measurements can enhance phase estimation accuracy without prior phase knowledge, outperforming classical and traditional squeezed states.

## Contribution

It introduces a method to generate and calibrate planar quantum squeezed states that provide a metrological advantage in phase estimation without prior phase information.

## Key findings

- PQS states achieve at least 3.1 dB advantage over classical states.
- PQS states outperform traditional squeezed states for most phase values.
- Spin-spin entanglement underpins the metrological advantage.

## Abstract

We study the generation of planar quantum squeezed (PQS) states by quantum non-demolition (QND) measurement of a cold ensemble of $^{87}$Rb atoms. Precise calibration of the QND measurement allows us to infer the conditional covariance matrix describing the $F_y$ and $F_z$ components of the PQS, revealing the dual squeezing characteristic of PQS. 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 gives a metrological advantage of at least 3.1 dB relative to classical states. The PQS also beats traditional squeezed states generated with the same QND resources, except for a narrow range of phase values. Using spin squeezing inequalities, we show that spin-spin entanglement is responsible for the metrological advantage.