Experimental Realization of Parrondo's Paradox in 1D Quantum Walks

Abstract

The Parrondo effect is a well‐known apparent paradox where a combination of biased random walks displays a counterintuitive reversal in direction. These random walks can be expressed in terms of classical coin tossing games, leading to the surprising result that a combination of losing games can result in a winning game. There is now a large body of literature on quantum walks theoretically analyzing the quantum version of this effect, but to date, there have been no experimental observations of quantum Parrondo walks. Here, the first experimental verification of a quantum Parrondo walk within a quantum optics scenario is demonstrated. Based on the compact large‐scale experimental quantum‐walk platform, two rotation operators are implemented to realize the quantum Parrondo effect. The effect of quantum coherence in a quantum Parrondo walk is also investigated based on a delayed‐choice scheme that cannot be realized with classical light. It is demonstrated that the Parrondo effect vanishes when the quantum walk has a completely decoherent initial state in a delayed‐choice setting. Quantum walks are fundamental to multiple quantum algorithms, and this research provides motivation to expand the results to further explore quantum Parrondo walks.

Generalized quantum teleportation of shared quantum secret with quantum walks

“…with S m = S. As the introduction of the new coins might produce some novel properties, the model has been studied widely [15][16][17] and been used as a tool to design some quantum communication protocols [18][19][20]36] and quantum Parrondo's game [22][23][24][25].…”

“…Here, we focus on coined QWs. Different classes of coined QWs have been explored in the past decades, such as QWs with many coins [14][15][16][17][18][19][20][21][22][23][24][25][26], multiple walkers [27][28][29][30][31][32][33][34][35][36][37][38][39], and nonhomogeneous coin operators [40][41][42][43][44][45][46][47][48][49][50][51]. Very recently, coined QWs have found several applications ranging from quantum computation [37,52,53] to quantum information [18-26, 36, 38, 39, 48-50, 54].…”

Parrondo's paradox in quantum walks with time-dependent coin operators

“…In this manuscript, we aim at implementing an actual Parrondo strategy with Quantum Walks(QWs) [25] as they are multi-purpose models with several possibilities for experimental realizations [26][27][28][29] and links with both fundamental [30] and applied [31][32][33][34] studies. To the best of our knowledge, the first attempts to set forth a Parrondian QW -considering a capital-dependent rule implemented with a position-dependent potential -were conveyed in Refs.…”

Study of Parrondo's paradox regions in one-dimensional quantum walks

“…However, the coherent character of the QW plays a vital role in the realization of a quantum Parrondo game. Recently, we have experimentally realized the quantum version of Parrondo effect [56], based on our currently developed compact large-scale QW platform [57].…”

“…Recent attempts [47,48,50] have been failed to realize the true Parrondo game in QWs for the case of a two-state coin (qubit) over the infinite steps. Decohering QW by introducing a pure dephasing channel can disappear the quantum Parrondo effect [56], indicates that coherence plays a key role in the emergence of the quantum Parrondo effect. In addition, we also discuss the relationship between quantum Parrondo's games and coin-position entanglement in our scenario.…”