  Incompatibility is a feature of quantum theory that sets it apart from
classical theory, and the inability to clone an unknown quantum state is one of
the most fundamental instances. The no-hiding theorem is another such instance
that arises in the context of the black-hole information paradox, and can be
viewed as being dual to no-cloning. Here, we formulate both of these
fundamental features of quantum theory in a single form that is amenable to
efficient verification, and that is robust to errors arising in state
preparation and measurements. We extend the notion of unitarity - an average
figure of merit that for quantum theory captures the coherence of a quantum
channel - to general physical theories. Then, we introduce the notion of
compatible unitarity pair (CUP) sets, that correspond to the allowed values of
unitarities for compatible channels in the theory. We show that a CUP-set
constitutes a simple 'fingerprint' of a physical theory, and that
incompatibility can be studied through them. We derive information-disturbance
constraints on quantum CUP-sets that encode both the no-cloning/broadcasting
and no-hiding theorems of quantum theory. We then develop randomised
benchmarking protocols that efficiently estimate quantum CUP-sets and provide
simulations using IBMQ of the simplest instance. Finally, we discuss ways in
which CUP-sets and quantum no-go theorems could provide additional information
to benchmark quantum devices.
