https://doi.org/10.1140/epjp/s13360-024-05050-0
Regular Article
Simulations of quantum walks on beam splitter arrays modeled as higher-order rotations
Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. Lago de Guadalupe Km. 3.5, C.P. 52926, Atizapán de Zaragoza, Estado de México, Mexico
Received:
26
September
2023
Accepted:
1
March
2024
Published online:
15
March
2024
We present a comprehensive matrix representation of a beam splitter array, incorporating multiple input and output channels. We propose treating each beam splitter as rotational matrices of a 2n-th-dimensional space. With these operators, the matrix that describes the entire square array and, consequently, the final probability distribution of an input photon state can be calculated. Furthermore, square and non-square arrays are explored using the same approach, encompassing certain interferometer arrays, the quantum quincunx, and the discrete quantum Zeno effect. In addition, we show the versatility of the proposed operator by using it to map the action of field operators in the description of multiphoton inputs.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
