Sensitivity to Initial Noise in Measurement-Induced Nonlinear Quantum Dynamics
- 31 Downloads
We consider a special iterated quantum protocol with measurement-induced nonlinearity for qubits, where all pure initial states on the Bloch sphere can be considered chaotic. The dynamics is ergodic with no attractive fixed cycles. We show that initial noise radically changes this behavior. The completely mixed state is an attractive fixed point of the dynamics induced by the protocol. Our numerical simulations strongly indicate that initially mixed states all converge to the completely mixed state. The presented protocol is an example, where gaining information from measurements and employing it to control an ensemble of quantum systems enables us to create ergodicity which, in turn, is destroyed by any initial noise.
Keywordspost-selection measurement chaos nonlinear quantum transformation
Unable to display preview. Download preview PDF.
- 1.P. Cvitanović, R. Artuso, R. Mainieri, et al., Chaos: Classical and Quantum, ChaosBook.org, Niels Bohr Institute, Copenhagen (2016).
- 11.J. W. Milnor, Dynamics in One Complex Variable, Princeton University Press (2006).Google Scholar
- 12.M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010).Google Scholar
- 13.J. W. Milnor, Dynamics on the Riemann Sphere, Eur. Math. Soc., Zürich (2006).Google Scholar
- 17.In preparation.Google Scholar