Quantum baker maps with controlled-NOT coupling

Abstract

The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting generalized baker map arises if the stacking orders for the factor maps are allowed to interact. These maps are readily quantized, in such a way that the stacking interaction is entirely attributed to primary qubits in each map, if each subsystem has power-of-two Hilbert space dimension. We here study the particular example of two baker maps that interact via a controlled-not interaction. Numerical evidence indicates that the control subspace becomes an ideal Markovian environment for the target map in the limit of large Hilbert space dimension.

8 pages

References in corpus (1)

• Entangling power of the quantum baker's map

Cited by in corpus (2)

• Matrix realignment and partial transpose approach to entangling power of quantum evolutions
• Statistical bounds on the dynamical production of entanglement