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The quantum baker map possesses two symmetries: a canonical "spatial"symmetry, and a time-reversal symmetry. We show that, even when these featuresare taken into account, the asymptotic entangling power of the baker's map doesnot always agree with the predictions of random matrix theory. We have verifiedthat the dimension of the Hilbert space is the crucial parameter whichdetermines whether the entangling properties of the baker are universal or not.For power-of-two dimensions, i.e., qubit systems, an anomalous entangling poweris observed; otherwise the behavior of the baker is consistent with randommatrix theories. We also derive a general formula that relates the asymptoticentangling power of an arbitrary unitary with properties of its reducedeigenvectors.Comment: 5 page

Entangling power of the baker’s map: Role of symmetries