Territories of Parrondo's paradox and its relation with entanglement in quantum walks

TL;DR

This paper explores how combining two losing quantum coin-tossing games in quantum walks can produce winning outcomes and generate maximal entanglement, revealing links between Parrondo's paradox and quantum entanglement.

Contribution

It demonstrates the realization of Parrondo's paradox in quantum walks and uncovers its connection to entanglement generation, offering insights for quantum algorithm development.

Findings

Losing quantum games can produce winning outcomes when combined.

Specific sequences and phases lead to maximal entanglement.

Regimes where Parrondo's effect and entanglement coincide are identified.

Abstract

Parrondo's paradox is a well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones. In this paper, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of different periods for distinct choices of the relative phase. Furthermore, we investigate the regimes of the relative phase of the initial state of coins where Parrondo games exist. Moreover, we also analyze the relationships between Parrondo's game and quantum entanglement and show regimes where the Parrondo sequence may generate a maximal entangler state in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.