  The area of property testing tries to design algorithms that can efficiently
handle very large amounts of data: given a large object that either has a
certain property or is somehow "far" from having that property, a tester should
efficiently distinguish between these two cases. In this survey we describe
recent results obtained for quantum property testing. This area naturally falls
into three parts. First, we may consider quantum testers for properties of
classical objects. We survey the main examples known where quantum testers can
be much (sometimes exponentially) more efficient than classical testers.
Second, we may consider classical testers of quantum objects. This is the
situation that arises for instance when one is trying to determine if quantum
states or operations do what they are supposed to do, based only on classical
input-output behavior. Finally, we may also consider quantum testers for
properties of quantum objects, such as states or operations. We survey known
bounds on testing various natural properties, such as whether two states are
equal, whether a state is separable, whether two operations commute, etc. We
also highlight connections to other areas of quantum information theory and
mention a number of open questions.
