Quantum Darwinism in a hazy environment

TL;DR

This paper explores how information about a quantum system can be obtained from a hazy environment, showing that initial entropy reduces the environment's capacity to store information but still allows system state inference with larger fragments.

Contribution

It demonstrates that even mixed, hazy environments can reveal system information, quantifying how initial entropy suppresses information storage capacity.

Findings

Information transfer is proportional to the environment's entropy increase.

Hazy environments require larger fragments to extract the same information.

System state can be inferred despite initial environment entropy.

Abstract

Quantum Darwinism recognizes that we - the observers - acquire our information about the "systems of interest" indirectly from their imprints on the environment. Here, we show that information about a system can be acquired from a mixed-state, or hazy, environment, but the storage capacity of an environment fragment is suppressed by its initial entropy. In the case of good decoherence, the mutual information between the system and the fragment is given solely by the fragment's entropy increase. For fairly mixed environments, this means a reduction by a factor 1-h, where h is the haziness of the environment, i.e., the initial entropy of an environment qubit. Thus, even such hazy environments eventually reveal the state of the system, although now the intercepted environment fragment must be larger by ~1/(1-h) to gain the same information about the system.