  The recently established resource theory of quantum coherence allows for a
quantitative understanding of the superposition principle, with applications
reaching from quantum computing to quantum biology. While different quantifiers
of coherence have been proposed in the literature, their efficient estimation
in today's experiments remains a challenge. Here, we introduce a collective
measurement scheme for estimating the amount of coherence in quantum states,
which requires entangled measurements on two copies of the state. As we show by
numerical simulations, our scheme outperforms other estimation methods based on
tomography or adaptive measurements, leading to a higher precision in a large
parameter range for estimating established coherence quantifiers of qubit and
qutrit states. We show that our method is accessible with today's technology by
implementing it experimentally with photons, finding a good agreement between
experiment and theory.
