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In "Distributed quantum sensing with mode-entangled spin-squeezed atomic states" Nature (2022) [1], Malia et. al. claim to improve the precision of a network of clocks by using entanglement. In particular, by entangling a clock network with up to four nodes, a precision 11.6 dB better than the quantum projection noise limit (i.e. precision without any entanglement) is reported. These claims are incorrect, Malia et. al. do not achieve an improved precision with entanglement. Here we show their demonstration is more than two orders of magnitude worse than the quantum projection noise limit.The central message in "Distributed quantum sensing with mode-entangled spin-squeezed atomic states" Nature (2022) [1] is that by entangling atoms in an atomic clock network, a precision is demonstrated that is impossible to attain using the same number of atoms and time without entanglement. Should we accept this message? Putting aside the impressive technical achievements in the paper, we can objectively assess whether the experimental data are in agreement with the claim.The final two figures of the paper present the supporting data. In Fig. 3, ∆( θ) is plotted as a function of the number of clocks M, each with N = 45, 000 atoms, where the black line (1/ √ MN ) is supposed to denote a limit that cannot be surpassed without entanglementthe quantum projection noise limit (QPN). One point should be made clear, ∆( θ) > 1/ √ MN is very definitively not the limit without entanglement. To see this requires an explanation of what ∆( θ) is. Despite the authors calling ∆( θ) the 'measured sensitivity', it is not a sensitivity at all. θ is simply the difference in values between two measurements (for M = 1).

We demonstrate that releasing atoms into free space from an optical lattice does not deteriorate cavitygenerated spin squeezing for metrological purposes. In this work, an ensemble of 500 000 spin-squeezed atoms in a high-finesse optical cavity with near-uniform atom-cavity coupling is prepared, released into free space, recaptured in the cavity, and probed. Up to ∼10 dB of metrologically relevant squeezing is retrieved for 700 μs free-fall times, and decaying levels of squeezing are realized for up to 3 ms free-fall times. The degradation of squeezing results from loss of atom-cavity coupling homogeneity between the initial squeezed state generation and final collective state readout. A theoretical model is developed to quantify this degradation and this model is experimentally validated.

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