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Quantum baker maps with controlled-NOT coupling

Raul O. Vallejos·P. R. del Santoro·A. M. Ozorio de Almeida
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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.

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Raul O. Vallejos, P. R. del Santoro, A. M. Ozorio de Almeida. 2006-03-23. Quantum baker maps with controlled-NOT coupling. https://doi.org/10.1088/0305-4470%2F39%2F18%2F028

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