# Implementing Parrondo's paradox with two coin quantum walks

## TL;DR

This paper demonstrates a genuine quantum Parrondo's paradox using two-coin quantum walks, highlighting the importance of initial state asymmetry and extending the analysis to three coins, with implications for quantum ratchet behavior.

## Contribution

It introduces a new approach to observe Parrondo's paradox in quantum walks using two coins, emphasizing initial state asymmetry, and extends the analysis to three coins.

## Key findings

- Genuine Parrondo's paradox observed with two-coin quantum walks.
- Asymmetry in initial state or shift operator is necessary.
- Extension of results to three-coin initial states.

## Abstract

Parrondo's paradox is ubiquitous in games, ratchets and random walks.The apparent paradox, devised by J.~M.~R.~Parrondo, that two losing games $A$ and $B$ can produce an winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo's paradox using quantum walks failed {for large number of steps}. In this work, we show that instead of a single coin if we consider a two coin initial state which may or may not be entangled, we can observe a genuine Parrondo's paradox with quantum walks. Further we focus on reasons for this and pin down the asymmetry in initial two-coin state or asymmetry in shift operator, either of which are necessary for observing a genuine Parrondo's paradox. We extend our work to a 3-coin initial state too with similar results. The implications of our work for observing quantum ratchet like behavior using quantum walks is also discussed.