# Enhancing test precision for local Lorentz symmetry violation with entanglement

## TL;DR

This paper proposes using specific entangled states, like NOON and Dicke states, to enhance the precision of tests for local Lorentz symmetry violation, offering practical methods for quantum metrology.

## Contribution

It introduces feasible entangled states for LSV testing that are robust, deterministically prepared, and can reach quantum-limited measurement precision.

## Key findings

- Dicke states are immune to magnetic field noise.
- Dicke states can achieve the standard quantum limit in LSV tests.
- NOON states can reach Heisenberg-limited precision.

## Abstract

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