The rich world of few qubit dynamics: chaos via measurements in the entanglement

Tamás Kiss
Wigner RC
Hungarian Academy of Sciences, Budapest

Deterministic chaos is generally prohibited in quantum mechanics, due to the unitary nature of the evolution. Measurements break unitarity and lead to an open system.
The information gained from the measurement can be used to select a part of an ensemble, this idea is utilized in entanglement purification protocols. The evolution 
can be deterministic, but non-unitary in this case. Iteratively applying such a scheme on single qubits leads to a special type of chaotic behavior, described by a map over the complex numbers [1].

Similar iterative dynamics for two qubits affects their entanglement. We prove that entanglement may evolve chaotically. A manifestation of complex chaos in this case is the sensitivity an all scales to the initial conditions, either leading to separable states or fully entangled states in the long time limit [2].

[1] T. Kiss, I. Jex, G. Alber, S. Vymetal,
Complex chaos in the conditional dynamics of qubits,
Phys. Rev. A 74, 040301(R) (2006). 

[2] T. Kiss, S. Vymetal, L. D. Toth, A. Gabris, I. Jex, G. Alber,
Measurement-Induced Chaos with Entangled States,
Phys. Rev. Lett. 107, 100501 (2011).