Investigation of quantum roulette

TL;DR

This paper introduces a general method for analyzing quantum roulette with any number of states using permutation and Fourier matrices, and examines environmental effects like depolarizing channels.

Contribution

It presents a novel, general approach to quantum roulette for arbitrary N-states, incorporating environmental interactions such as depolarizing channels.

Findings

The method effectively solves quantum roulette for N=3.

Environmental effects impact the strategy's performance.

The approach generalizes previous specific-case analyses.

Abstract

In this paper, by using permutation matrices as a representation of symmetric group $S_N$ and Fourier matrix, we investigate quantum roulette with an arbitrary $N$-state. This strategy, which we introduce, is general method that allows us to solve quantum game for an arbitrary $N$-state. We consider the interaction between the system and its environment and study the effect of the depolarizing channel on this strategy. Finally, as an example we employ this strategy for quantum roulette with N=3.