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Recently, the emergence of classical objectivity as a property of a quantumstate has been explicitly derived for a small object embedded in a photonicenvironment in terms of a spectrum broadcast form---a specific classicallycorrelated state, redundantly encoding information about the preferred statesof the object in the environment. However, the environment was in a pure stateand the fundamental problem was how generic and robust is the conclusion. Herewe prove that despite of the initial environmental noise the emergence of thebroadcast structure still holds, leading to the perceived objectivity of thestate of the object. We also show how this leads to a quantum Darwinism-typecondition, reflecting classicality of proliferated information in terms of alimit behavior of the mutual information. Quite surprisingly, we find,,singular points'' of the decoherence, which can be used to faithfullybroadcast a specific classical message through the noisy environment.

Objectivity in the Photonic Environment Through State Information Broadcasting