Quantum Parrondo Games in Low-Dimensional Hilbert Spaces
Quantum Physics
2023-06-30 v1
Abstract
We consider quantum variants of Parrondo games on low-dimensional Hilbert spaces. The two games which form the Parrondo game are implemented as quantum walks on a small cycle of length . The dimension of the Hilbert space is . We investigate a random sequence of these two games which is realized by a quantum coin, so that the total Hilbert space dimension is . We show that in the quantum Parrondo game constructed in this way a systematic win or loss occurs in the long time limit. Due to entaglement and self-interference on the cycle, the game yields a rather complex structure for the win or loss depending on the parameters.
Keywords
Cite
@article{arxiv.2306.16845,
title = {Quantum Parrondo Games in Low-Dimensional Hilbert Spaces},
author = {Andreas Mielke},
journal= {arXiv preprint arXiv:2306.16845},
year = {2023}
}