Entangling power of the baker's map: Role of symmetries (6 pages)

Lieven Clarisse

Mario Salerno, Vladislav Popkov

R. Shankar

Rômulo F. Abreu, Raúl O. Vallejos

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.

Andrea Fratalocchi

A J Scott, Carlton M. Caves

We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits and two proposals for a measure of multipartite entanglement. Also derived are some new analytical formulae describing the levels of entanglement expected in random pure states.