  In their paper "Time-reversal-based quantum metrology with many-body
entangled states" Nature Physics (2022), Colombo et. al. claim to measure both
an unknown phase and an oscillating magnetic field with a precision that cannot
be achieved using independent particles - a limit known as the standard quantum
limit. By entangling an ensemble of $\sim300$ atoms, Colombo et. al. measure an
angle of rotation away from a known initial state and additionally measure a
magnetic field oscillating at 290 Hz. The authors report an experimental
precision approximately a factor of 4 beyond what is possible with the same
number of independent atoms (12.8 dB and 11.8 dB for these tasks respectively).
These claims are incorrect. Colombo et. al. do not surpass the precision bound
for 300 independent particles, nor do they even surpass the precision bound for
a single particle. Colombo et. al. cite several experiments that surpass the
standard quantum limit using entanglement. Each and every paper cited performs
incorrect, incomplete or misleading comparisons of the type that we highlight
here. The consequence being that the single particle precision bound has never
been experimentally surpassed with entanglement.
