Quantifying coherence of quantum measurements
In this work we investigate how to quantify the coherence of quantum
measurements. First, we establish a resource theoretical framework to address
the coherence of measurement and show that any statistical distance can be
adopted to define a coherence monotone of measurement. For instance, the
relative entropy fulfills all the required properties as a proper monotone. We
specifically introduce a coherence monotone of measurement in terms of
off-diagonal elements of Positive-Operator-Valued Measure (POVM) components.
This quantification provides a lower bound on the robustness of
measurement-coherence that has an operational meaning as the maximal advantage
over all incoherent measurements in state discrimination tasks. Finally, we
propose an experimental scheme to assess our quantification of
measurement-coherence and demonstrate it by performing an experiment using a
single qubit on IBM Q processor.
Kyunghyun Baek Adel Sohbi Jaehak Lee Jaewan Kim Hyunchul Nha