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Experimental Implementation of a NMR NOON State Thermomete

Utilizing the highly correlated quantum NOON states of particles, we have implemented a proof-of-principle quantum thermometer using the NMR technique for measuring the variation of local magnetic field with the temperature variation. The system used was the star-topology system of hexafluorophosphate molecules and the thermometer showed a sensitivity of $85nT/ ^o C$. Using the hexafluorophosphate and the trimethylphosphite spin systems, we have quantified the advantage of the quantum protocol over the classical one for measuring magnetic field. The quantum protocol showed the best performance for a time evolution in the quantum circuit of $T = 20ms$, where the errors in the measurement scaled as the Heisenberg limit $1/N$.