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When quantum information is spread over a system through nonclassicalcorrelation, it makes retrieving information by local measurementsdifficult---making global measurement necessary for optimal parameterestimation. In this paper, we consider temperature estimation of a system in aGibbs state and quantify the separation between the estimation performance ofthe global optimal measurement scheme and a greedy local measurement scheme bydiagonal quantum discord. In a greedy local scheme, instead of globalmeasurements, one performs sequential local measurement on subsystems, which ispotentially enhanced by feed-forward communication. We show that, forfinite-dimensional systems, diagonal discord quantifies the difference in thequantum Fisher information quantifying the precision limits for temperatureestimation of these two schemes, and we analytically obtain the relation in thehigh-temperature limit. We further verify this result by employing the examplesof spins with Heisenberg's interaction.

Quantifying precision loss in local quantum thermometry via diagonal discord