22-30 July 2021
North-West University
Africa/Johannesburg timezone
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Generating function approach to open quantum walks

26 Jul 2021, 11:30
Potchefstroom Campus (North-West University)

Potchefstroom Campus

North-West University

Oral Presentation Track G - Theoretical and Computational Physics Theoretical and Computational Physics


Mr Ayanda Zungu (Department of Physics, North-West University, Mafikeng Campus)


Open quantum walks (OQWs) have been introduced as a type of quantum walks which are entirely driven by the dissipative interaction with external environments and are defined in terms of discrete completely positive trace-preserving maps on graphs [1]. Recently, a quantum optical scheme for the experimental realization of OQWs was proposed [2]. In the proposed scheme, a two-level atom plays the role of the "walker" and the Fock states of the cavity mode correspond to the lattice sites of the OQW. Using the small unitary rotations approach and rotating wave approximation the effective dynamics of the system is shown to be an OQW. The presence of spontaneous emission in the system was an essential ingredient for obtaining an OQW. In this contribution, we solve this OQW analytically using generating functions. We used the obtained solution to construct the moments of this quantum walk explicitly. The dynamics of the observables (mean, variance) are presented for various parameters.

Keywords: Open quantum walks; quantum optics; quantum dynamics engineering.


[1] S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy, J. Stat. Phys. 147 (2012), 832.
[2] I. Sinayskiy and F. Petruccione, Int. J. Quantum Inform. 12 (2014), 1461010.

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Primary author

Mr Ayanda Zungu (Department of Physics, North-West University, Mafikeng Campus)


Prof. Ilya Sinayskiy (School of Physics and NITheP, University of KwaZulu-Natal) Prof. Francesco Petruccione

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