  We introduce an entanglement-depth criterion optimized for planar quantum
squeezed (PQS) states. It is connected with the sensitivity of such states for
estimating an arbitrary, not necessarily small phase. We compare numerically
our criterion with the well-known extreme spin squeezing condition of
S{\o}rensen and M{\o}lmer [Phys. Rev. Lett. 86, 4431 (2001)] and show that our
condition detects a higher depth of entanglement when both planar spin
variances are squeezed below the standard quantum limit. We employ our theory
to monitor the entanglement dynamics in a PQS state produced via quantum
non-demolition (QND) measurements using data from a recent experiment [Phys.
Rev. Lett. 118, 233603 (2017)].
