Figure 1
Quantum Darwinism can be illustrated using a model introduced in
12. The system
, a spin-
particle, interacts with
two-dimensional subsystems of the environment through
for a time
. The initial state of
is
. All the plotted quantities are functions of the system’s observable
, where
is the angle between eigenstates of
and the pointer states of
—here the eigenstates of
. (a) Information acquired by the optimal measurement
on the whole environment,
, as a function of the inferred observable
and the action
for all
. A large amount of information is accessible in the whole environment for any observables
except when the interaction action
is very small. Thus, complete imprinting of an observable of
in
is not sufficient to claim objectivity. (b) Redundancy of the information about the system as a function of the inferred observable
and the action
. It is measured by
, which counts the number of times 90% of the total information can be “read off” independently by measuring distinct fragments of the environment. For all values of the action
, redundant imprinting is sharply peaked around the pointer observable. Redundancy is a very selective criterion. The number of copies of relevant information is high only for the observables
falling inside the theoretical bound (see text) indicated by the dashed line. (c) Information about
extracted by an observer restricted to local random measurements on
environmental subsystems (e.g.,
, where each
is chosen at random). The interaction action
is randomly chosen in
for each
. Because of redundancy, pointer states—and only pointer states—can be found out through this far-from-optimal measurement strategy. Information about any other observable
is restricted by our theorem to be equal to the information about it contained in the pointer observable
, Eq. (
6).
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