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We show that the lowest quantum Cram\'{e}r-Rao bound achievable ininterferometry with a one-axis twisted spin coherent state is saturated by theasymptotic method of moments error of a protocol that uses one call to theone-axis twisting, one call to time-reversed one-axis twisting, and a finaltotal spin measurement (i.e., a twist-untwist protocol). The result is derivedby first showing that the metrological phase diagram for one-axis twisting isasymptotically characterized by a single QFI value $N(N+1)/2$ for all times,then constructing a twist-untwist protocol having a method of moments errorthat saturates this value. The case of finite-range one-axis twisting issimilarly analyzed, and a simple functional form for the metrological phasediagram is found in both the short-range and long-range interaction regimes.Numerical evidence suggests that the finite-range analogues of twist-untwistprotocols can exhibit a method of moments error that asymptotically saturatesthe lowest quantum Cram\'{e}r-Rao bound achievable in interferometry withfinite-range one-axis twisted spin coherent states for all interaction times.

Saturating the one-axis twisting quantum Cram\'{e}r-Rao bound with a total spin readout