  In this paper, we study the following question: given a black box performing
some unknown quantum measurement on a multi-qudit system, how do we test
whether this measurement has certain property or is far away from having this
property. We call this task \textit{property testing} of quantum measurement.
We first introduce a metric for quantum measurements, and show that it
possesses many nice features. Then we show that, with respect to this metric,
the following classes of measurements can be efficiently tested: 1. the
stabilizer measurements, which play a crucial role for quantum error
correction; 2. the $k$-local measurements, i.e. measurements whose outcomes
depend on a subsystem of at most $k$ qudits; 3. the permutation-invariant
measurements, which include those measurements used in quantum data
compression, state estimation and entanglement concentration. In fact, all of
them can be tested with query complexity independent of the system's dimension.
Furthermore, we also present an algorithm that can test any finite set of
measurements. Finally, we consider the following natural question: given two
black-box measurement devices, how do we estimate their distance? We give an
efficient algorithm for this task, and its query complexity is also independent
of the system's dimension. As a consequence, we can easily test whether two
unknown measurements are identical or very different.
