  Given a bipartite quantum state rho with subsystems A and B of arbitrary
dimensions, we study the entanglement detecting capabilities of locally
noneffective, or cyclic, unitary operations [L. B. Fu, Europhys. Lett., vol.
75, pp. 1-7, 2006]. Local cyclic unitaries have the special property that they
leave their target subsystem invariant. We investigate the distance between rho
and the global state after local application of such unitaries as a possible
indicator of entanglement. To this end, we derive and discuss closed formulae
for the maximal such distance achievable for three cases of interest:
(pseudo)pure quantum states, Werner states, and two-qubit states. What makes
this criterion interesting, as we show here, is that it surprisingly displays
behavior similar to recent anomalies observed for non-locality measures in
higher dimensions, as well as demonstrates an equivalence to the CHSH
inequality for certain classes of two-qubit states. Yet, despite these
similarities, the criterion is not itself a non-locality measure. We also
consider entanglement detection in bound entangled states.
