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We study a distinction problem of two heat baths with given information from ancilla (quantum or classical two level system) which is interacting with the heat baths. Analysing dynamics of ancilla system in a Markov approximation region, we show that the process in which“quantum ancilla” acquires the quantum distinguishability is described as a bifurcation process from the time evolution of classical distinguishability.

A Dynamical Bifurcation of Distinguishability in Thermalization Processes, from Classical to Quantum