Uniqueness of the Observable Leaving Redundant Imprints in the Environment in the Context of Quantum Darwinism

TL;DR

This paper investigates the conditions under which the observable leaving redundant imprints in the environment in quantum Darwinism is unique, demonstrating that within certain partitions this observable is uniquely determined, clarifying the interpretational ambiguities.

Contribution

The paper proves a uniqueness theorem for the observable leaving redundant imprints in quantum Darwinism, identifying conditions for its physical significance.

Findings

Within specific environment partitions, the pointer observable is uniquely determined.

Partitions outside the identified subset generally lack physical significance.

The results clarify the interpretational ambiguity in quantum Darwinism.

Abstract

In quantum Darwinism, the pointer observable of a system leaves redundant imprints in its environment after decoherence. Each imprint is recorded in a fraction of the environment, which identifies a particular partition of the environment. An ambiguity situation may occur when another observable noncommuting to the pointer observable also leaves redundant imprints with respect to another partition of the environment. We study this problem based on a uniqueness theorem we proved. We find that within a particular subset of all possible partitions of the environment, the observable of the system leaving redundant and nondegenerately recorded imprints in the environment is unique. And, in a typical situation, the partitions outside this particular subset have no physical significance.