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Strongly lensed gravitational waves (GWs) from binary coalescence manifest asrepeated chirps from the original merger. At the detectors, the phase of thelensed GWs and its arrival time differences will be consistent modulo a fixedconstant phase shift. We develop a fast and reliable method to efficientlyreject event pairs that are not-lensed copies and appropriately rank the mostinteresting candidates. Our method exploits that detector phases are the bestmeasured GW parameter, with errors only of a fraction of a radian anddifferences across the frequency band that are better measured than the chirpmass. The arrival time phase differences also avoid the shortcomings of lookingfor overlaps in highly non-Gaussian sky maps. Our basic statistic determiningthe consistency with lensing is the distance between the phase posteriors oftwo events and it directly provides information about the lens-source geometrywhich helps inform electromagnetic followups. We demonstrate that for simulatedsignals of not-lensed binaries specifically chosen with many coincidentproperties so as to trigger false lensing alarms none of the pairs have phasescloser than $3\sigma$, and most cases reject the lensing hypothesis by$5\sigma$. Looking at the latest catalog, GWTC3, we find that only $6\%$ of thepairs are consistent with lensing at 99\% confidence level. Moreover, we rejectabout half of the pairs that would otherwise favor lensing by their parameteroverlaps and demonstrate good correlation with detailed joint parameterestimation results. This reduction of the false alarm rate will be of paramountimportance in the upcoming observing runs and the eventual discovery of lensedGWs. Our code is publicly available and could be applied beyond lensing to testpossible deviations in the phase evolution from modified theories of gravityand constrain GW birefringence.

Identifying strongly lensed gravitational waves through their phase consistency