Entangling power of the baker’s map: Role of symmetries
Rômulo F. Abreu, Raúl O. Vallejos · Physical Review A · 2006
The quantum baker map possesses two symmetries: a canonical ``spatial'' symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always agree with the predictions of random matrix theory. We have verified that the dimension of the Hilbert space is the crucial parameter that determines whether the entangling properties of the baker map are universal or not. For power-of-2 dimensions, i.e., qubit systems, an anomalous entangling power is observed; otherwise the behavior of the baker map is consistent with random matrix theories. We also derive a general formula that relates the asymptotic entangling power of an arbitrary unitary with properties of its reduced eigenvectors.