  The goal of quantum metrology is to improve measurements' sensitivities by
harnessing quantum resources. Metrologists often aim to maximize the quantum
Fisher information, which bounds the measurement setup's sensitivity. In
studies of fundamental limits on metrology, a paradigmatic setup features a
qubit (spin-half system) subject to an unknown rotation. One obtains the
maximal quantum Fisher information about the rotation if the spin begins in a
state that maximizes the variance of the rotation-inducing operator. If the
rotation axis is unknown, however, no optimal single-qubit sensor can be
prepared. Inspired by simulations of closed timelike curves, we circumvent this
limitation. We obtain the maximum quantum Fisher information about a rotation
angle, regardless of the unknown rotation axis. To achieve this result, we
initially entangle the probe qubit with an ancilla qubit. Then, we measure the
pair in an entangled basis, obtaining more information about the rotation angle
than any single-qubit sensor can achieve. We demonstrate this metrological
advantage using a two-qubit superconducting quantum processor. Our measurement
approach achieves a quantum advantage, outperforming every entanglement-free
strategy.
