Optimal omni-directional field sensing with entangled states

A qubit (spin-half system) subject to an unknown rotation serves as a paradigmatic setup for studying fundamental limits in quantum metrology. The optimal quantum Fisher information about the parameter is obtained when the spin is prepared in a state that maximizes the variance of the operator that induces the rotation. However, if the rotation angle is unknown an optimal single-qubit sensor cannot be prepared. In this work, inspired by simulations of closed time-like curves, we circumvent this limitation, achieving the optimal quantum Fisher information about a rotation angle for any rotation axis. To achieve this result, we prepare the probe qubit in an entangled state with an ancilla qubit, then measure the pair in an entangled basis, obtaining more information about the rotation than achievable with a single-qubit sensor. We demonstrate this metrological advantage using a two-superconducting-qubit quantum processor.