Non UBC
DSpace
Tamás Kiss
2019-10-21T08:24:56Z
2019-04-23T11:01
Quantum informational protocols involve coherent evolution, measurement, and postselection of qubits. A typical example is entanglement distillation. The resulting conditional dynamics is nonlinear, in contrast to the usual evolution of both closed and open quantum systems. Already the simplest types of such protocols may result in rich, complex chaotic dynamics when applied iteratively. An important property of these iterated dynamical systems is that initially pure quantum states remain pure throughout the evolution. For single-qubit systems, there is a one to one correspondence of the pure-state quantum dynamics to the iterated dynamics of quadratic rational maps with one complex variable. For two-qubit systems LOCC operations may lead to dynamics, where the evolution of entanglement is chaotic in the sense of crucially depending infinitely fine details of the initial state. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. They provide for example a solution to the quantum state matching problem, i.e. the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We determine that such protocols may exhibit sensitive, quasi-chaotic evolution not only for pure initial states but also for mixed states, i.e., the complex dynamical behavior is not destroyed by small initial uncertainty. We show that the appearance of sensitive, complex dynamics associated with a fractal structure in the parameter space of the system has the character of a phase transition. The purity of the initial state plays the role of the control parameter, and the dimension of the fractal structure is independent of the purity value after passing the phase transition point.
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References
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[1] A. GilyÃ©n, T. Kiss, and I. Jex, Sci. Rep. 6, 20076 (2016).
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[2] O. KÃ¡lmÃ¡n and T. Kiss, Phys. Rev. A 97, 032125 (2018).
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[3]Martin Malachov, Igor Jex, Orsolya KÃ¡lmÃ¡n, and TamÃ¡s Kiss, Chaos 29, 033107 (2019).
https://circle.library.ubc.ca/rest/handle/2429/71979?expand=metadata
56.0 minutes
video/mp4
Author affiliation: Wigner Research Centre for Physics Hungary
Banff (Alta.)
10.14288/1.0384613
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Quantum theory
Mathematical physics
Measurement induced complex chaos in quantum protocols
Moving Image
http://hdl.handle.net/2429/71979