Comment on 'Collectively enhanced quantum measurements at the Heisenberg limit'

In a seminal paper [8] it was shown that Heisenberg-limited measurements could be achieved without using entangled states by coupling the quantum resources to a common environment that could be measured, at least, in part. The authors also claimed that their method would be robust under decoherence, and, in particular, applied it to derive an analytical expression to measure the change in length of an optical cavity within the Tavis-Cummings model using the superradiance approximation, which would still have a 1/N scaling. Here, we show that the analytical derivations in [8] are incompatible with the cavity superradiance, leading to the standard quantum-limited scaling 1/\sqrt{N}.