  Phase estimation is one of the most important facets of quantum metrology,
with applications in sensing, microscopy, and quantum computation. When
estimating a phase shift in a lossy medium, there is an upper bound on the
attainable information per particle sent through the phase shift. Previously,
only entanglement-enhanced measurements have been shown to saturate this bound.
We introduce a measurement scheme which can saturate the bound without relying
on entanglement.
