Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits

TL;DR

This paper develops proper methods for quantizing history-dependent Parrondo games, Markov processes, and multiplexing circuits within quantum information theory, ensuring faithful quantum analogs of classical constructions.

Contribution

It introduces a systematic approach for properly quantizing classical stochastic processes and circuits in quantum settings, maintaining their original structure.

Findings

Proper quantum versions of Parrondo games are constructed.

Quantum analogs of Markov processes are developed.

Multiplexing circuits are extended to quantum frameworks.

Abstract

In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done "properly", a faithful copy of the original construction is required to exist within the new "quantum" one, just as is required when a function is extended to a larger domain. Here procedures for extending history dependent Parrondo games, Markov processes and multiplexing circuits to their "quantum" versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed.