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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 MM. The dimension of the Hilbert space is 2M2M. We investigate a random sequence of these two games which is realized by a quantum coin, so that the total Hilbert space dimension is 4M4M. 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}
}
R2 v1 2026-06-28T11:17:46.961Z