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A recent proposal for testing Lorentz symmetry violation (LSV) presents aformulation where the effect of violation is described as a local interaction[R. Shaniv, et al, Phys. Rev. Lett. 120, 103202 (2018)]. An entangled ion pairin a decoherence free subspace (DFS) is shown to double the signal to noiseratio (SNR) of one ion, while (even)-N/2 such DFS pairs in a collectiveentangled state improve SNR by N times, provided the state parity or theeven/odd numbers of ions can be measured. It remains to find out, however, howsuch fiducial entangled states can be prepared at nonexponentially smallsuccess rates. This work suggests two types of many particle entangled statesfor testing LSV: the maximally entangled NOON state, which can achieveHeisenberg limited precision; and the balanced spin-1 Dicke state, which isreadily available in deterministic fashion. We show that the latter also livesin a DFS and is immune to stray magnetic fields. It can achieve classicalprecision limit or the standard quantum limit (SQL) based on collectivepopulation measurement without individual atom resolution. Given the highinterests in LSV and in entanglement assisted quantum metrology, ourobservation offers additional incentives for pursuing practical applications ofmany atom entangled states.

Enhancing test precision for local Lorentz symmetry violation with entanglement