Laser sensors incorporating fast light or exceptional points (EPs) have demonstrated increased scale-factor sensitivity, but have yet to demonstrate a corresponding increase in measurement precision due to excess noise. We find that in the linear regime, EPs are rotationally invariant and so do not boost precision, regardless of the type of EP. This limit also applies above threshold to EP systems that use dissipative coupling, which explains recent experiments in conventional laser gyroscopes that found no increase in precision at the deadband edge. However, above threshold the rotational symmetry of EPs can be broken by gain saturation. We find that EPs in conservatively-coupled systems with a saturation imbalance can lead to an increase in precision.
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