  Wave-particle duality relations express the fact that knowledge about the
path a particle took suppresses information about its wave-like properties, in
particular, its ability to generate an interference pattern. Recently, duality
relations in which the wave-like properties are quantified by using measures of
quantum coherence have been proposed. Quantum coherence can be generalized to a
property called group asymmetry. Here we derive a generalized duality relation
involving group asymmetry, which is closely related to the success probability
of discriminating between the actions of the elements of a group. The second
quantity in the duality relation, the one generalizing which-path information,
is related to information about the irreducible representations that make up
the group representation.
