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Measurement induced complex chaos in quantum protocols
Measurement induced complex chaos in quantum protocols
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When 
Apr 18, 2019 from 01:00 pm to 02:00 pm 
Speaker  Tamas Kiss 
Speaker Information  Hungarian Academy of Sciences, Wigner Research Center for Physics Budapest, Hungary 
Where  612 HN 
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Abstract:
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 singlequbit systems, there is a one to one correspondence of the purestate quantum dynamics to the iterated dynamics of quadratic rational maps with one complex variable. For twoqubit 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 nonlinear 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, quasichaotic 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.
A. Gilyén, T. Kiss, and I. Jex, Sci. Rep. 6, 20076 (2016).
O. Kálmán and T. Kiss, Phys. Rev. A 97, 032125 (2018).
Martin Malachov, Igor Jex, Orsolya Kálmán, and Tamás Kiss, Chaos 29, 033107 (2019).