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Parrondo's paradox in space-inhomogeneous quantum walks
Zbigniew Walczak1, Jarosław H Bauer1
1University of Lodz, Department of Theoretical Physics, Faculty of Physics and Applied Informatics, Pomorska 149/153, 90-236 Lodz, Poland.
Physical Review. E
|August 1, 2025
Summary
Parrondo's paradox, where decreasing dynamics combine to increase a quantity, is demonstrated in quantum walks. This paradox impacts quantum entanglement differently in homogeneous versus inhomogeneous settings.
Area of Science:
- Quantum mechanics
- Quantum information theory
- Complex systems
Background:
- Parrondo's paradox describes a phenomenon where combining losing strategies results in a winning strategy.
- Quantum walks are a quantum analogue of classical random walks, with applications in quantum computing and algorithms.
- Quantum entanglement is a key resource in quantum information processing, representing a non-classical correlation between quantum systems.
Purpose of the Study:
- To investigate the occurrence and characteristics of Parrondo's paradox in one-dimensional discrete-time quantum walks.
- To explore whether Parrondo's paradox can manifest in both homogeneous and space-inhomogeneous quantum walks.
- To analyze the distinct effects of Parrondo's paradox on the time evolution of quantum entanglement in different quantum walk scenarios.
Main Methods:
- Theoretical analysis of one-dimensional discrete-time quantum walks.
- Mathematical modeling of homogeneous and space-inhomogeneous quantum walk dynamics.
- Quantification of quantum entanglement evolution under Parrondo's paradox conditions.
Main Results:
- Parrondo's paradox is shown to occur in both homogeneous and space-inhomogeneous one-dimensional discrete-time quantum walks.
- The manifestation of Parrondo's paradox differs between homogeneous and space-inhomogeneous quantum walks.
- The impact of Parrondo's paradox on the time evolution of quantum entanglement is distinct in homogeneous and space-inhomogeneous quantum walks.
Conclusions:
- Parrondo's paradox is a viable phenomenon in various quantum walk models, extending beyond classical systems.
- The spatial properties of quantum walks significantly influence how Parrondo's paradox affects quantum entanglement.
- This research offers new insights into the interplay between paradoxes, quantum dynamics, and entanglement in quantum information science.
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