  Quantum nonlocality is associated with the local indistinguishability of
orthogonal states. Unextendible product basis (UPB), a widely used tool in
quantum information, exhibits nonlocality which is the powerful resource for
quantum information processing. In this work we extend the definitions of
nonlocality and genuine nonlocality from states to operators. We also extend
UPB to the notions of unextendible product operator basis, unextendible product
unitary operator basis (UPUOB) and strongly UPUOB. We construct their examples,
and show the nonlocality of some strongly UPUOBs under local operations and
classical communications. We study the phenomenon of these operators acting on
quantum states. As an application, we distinguish the two-dimensional strongly
UPUOB which only consumes three ebits of entanglement. Our results imply that
such UPUOBs exhibit nonlocality as UPBs and the distinguishability of them
requires entanglement resources.
