  In many experiments on microscopic quantum systems, it is implicitly assumed
that when a macroscopic procedure or "instruction" is repeated many times --
perhaps in different contexts -- each application results in the same
microscopic quantum operation. But in practice, the microscopic effect of a
single macroscopic instruction can easily depend on its context. If undetected,
this can lead to unexpected behavior and unreliable results. Here, we design
and analyze several tests to detect context-dependence. They are based on
invariants of matrix products, and while they can be as data intensive as
quantum process tomography, they do not require tomographic reconstruction, and
are insensitive to imperfect knowledge about the experiments. We also construct
a measure of how unitary (reversible) an operation is, and show how to estimate
the volume of physical states accessible by a quantum operation.
