Nonclassical correlations for quantum metrology in thermal equilibrium

Nonclassical correlations beyond entanglement might provide a resource in quantum information tasks, such as quantum computation or quantum metrology. Quantum discord is a measure of nonclassical correlations to which entanglement belongs as a subset. Exploring the operational meaning of quantum discord as a resource in quantum information processing tasks, such as quantum metrology, is of essential importance to our understanding of nonclassical correlations. In our recent work [Phys. Rev. A 98, 012115 (2018)], we considered a protocol—which we call the greedy local thermometry protocol—for estimating the temperature of thermal equilibrium states from local measurements, elucidating the role of diagonal discord in enhancing the protocol sensitivity in the high-temperature limit. In this paper, we extend our results to a general greedy local parameter estimation scenario. In particular, we introduce a quantum discord—which we call discord for local metrology—to quantify the nonclassical correlations induced by the local optimal measurement on the subsystem. We demonstrate explicitly that discord for local metrology plays a role in sensitivity enhancement in the high-temperature limit by showing its relation to loss in quantum Fisher information. In particular, it coincides with diagonal discord for estimating a linear coupling parameter.

Figure 1

Global measurement and greedy local measurement scheme: One first measures a subsystem $A$ with the local optimal measurement in the sense of the local QFI and then measures the other subsystem $B$ in order to estimate an unknown parameter $\xi$. The constrained QFI is given as ${\mathcal{F}}_{A\to B}\left(\xi \right)={\mathcal{F}}_A\left(\xi \right)+{\mathcal{F}}_{B|A}\left(\xi \right)$. We explore the relation between the quantum discord $D_{A\to B}\left(\xi \right)$ and the precision loss $\mathrm{\Delta }\mathcal{F}\left(\xi \right)={\mathcal{F}}_{AB}\left(\xi \right)-{\mathcal{F}}_{A\to B}\left(\xi \right)$.