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The objective, classical world emerges from the underlying quantum substratevia the proliferation of redundant copies of selected information into theenvironment, which acts as a communication channel, transmitting thatinformation to observers. These copies are independently accessible, allowingmany observers to reach consensus about the state of a quantum system via itsimprints in the environment. Quantum Darwinism recognizes that the redundancyof information is thus central to the emergence of objective reality in thequantum world. However, in addition to the "quantum system of interest," thereare many other systems "of no interest" in the Universe that can imprintinformation on the common environment. There is therefore a danger that theinformation of interest will be diluted with irrelevant bits, suppressing theredundancy responsible for objectivity. We show that mixing of the relevant(the "wheat") and irrelevant (the "chaff") bits of information makes littlequantitative difference to the redundancy of the information of interest. Thus,we demonstrate that it does not matter whether one separates the relevantinformation) from the (irrelevant) chaff: The large redundancy of the relevantinformation survives dilution, providing evidence of the objective, effectivelyclassical world.

Redundancy of einselected information in quantum Darwinism: The irrelevance of irrelevant environment bits