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

## TL;DR

This paper demonstrates that irrelevant environmental information does not significantly affect the redundancy of relevant information in quantum Darwinism, supporting the robustness of objective classical reality emergence.

## Contribution

It shows that mixing relevant and irrelevant information in the environment does not diminish the redundancy of the relevant information, affirming the resilience of quantum Darwinism.

## Key findings

- Redundant information of interest remains intact despite irrelevant bits.
- Mixing relevant and irrelevant information does not significantly reduce redundancy.
- Objective classical reality emerges robustly from quantum substrate.

## Abstract

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