A game theoretic approach to quantizing Markov processese

In the context of quantum information theory, “quantization” of various mathematical 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, Markov processes that serve as mathematical models of history dependent Parrondo games are quantized properly.