Complex chaox in conditional qubit dynamics and purification protocols

T. Kiss, Igor Jex, G. Alber +1 more

Cheng‐Chen Luo, Lan Zhou, Wei Zhong +1 more

S. Vymětal, T. Kiss, Igor Jex +5 more

The presence of complex chaos in iterative applications of selective dynamics on quantum systems is a novel form of quantum chaos with true sensitivity to initial conditions. Techniques for the study of pure states are extended to the two‐qubit case.

T. Kiss, Igor Jex, G. Alber +1 more

Complex chaos is specified by an iterated mapping on complex numbers. It has recently been found in the dynamics of qubits where each time step is conditioned on a measurement result on part of the system. We analyse the simplest case of one qubit dynamics with one complex parameter in some detail. We point out that two attractive cycles can exist and provide examples how the fractal like Julia set divides the areas of corresponding initial states. We show how to determine the set of parameters for which one, two or no stable fixed cycles exists and provide the numerically calculated images of the sets. The results can be relevant for the quantum state purification protocol based on the similar dynamics of two or more qubits and in general for any protocol based on conditioned nonlinear dynamics where truly chaotic behavior may occur.

Yilun Guan, Duy Quang Nguyen, Jingwei Xu +1 more

Entanglement-purification protocols, developed for the sake of high-fidelity communication through noisy quantum channels, are highly nonlinear quantum operations and can offer a very useful context to studies of nonlinear complex maps. Recently it was demonstrated that the feedback mechanism used in a typical purification protocol can cause the evolution dynamics of qubits to exhibit chaos [Kiss et al., Phys. Rev. Lett. 107, 100501 (2011)]. In this work we extend the investigation by considering the natural time evolution of qubits during a purification process, leading to a number of interesting findings that reflect the competition between the natural unitary evolution of qubits and nonlinear purification operations. As a result, the overall evolution dynamics of entanglement can be much richer. Possible applications are also proposed.