Estimating Coherence Measures from Limited Experimental Data Available

Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to estimate these coherence measures in experiments. This is a challenging task, since the state of a system is often unknown in practical applications and the accessible measurements in a real experiment are typically limited. In this Letter, we put forward an approach to estimate coherence measures of an unknown state from any limited experimental data available. Our approach is not only applicable to coherence measures but can be extended to other resource measures.

Figure 1

Plots of ${\max }_{(\mu ,\nu )\ge 0}{\mathcal{F}}_{S_k,T_k}(\mu ,\nu )$ with $S_k$ containing $L_k=100k$ states and $T_k=20k^2$: (a) for $C_{l_1}$ and (b) for $C_g$. Solid lines represent the analytical results. The plots illustrate that ${\max }_{(\mu ,\nu )\ge 0}{\mathcal{F}}_{S_k,T_k}(\mu ,\nu )$ becomes closer and closer to $C^{\mathrm{LB}}$ as $L_k$ and $T_k$ increase.