Origin and Limit of the Recovery of Damaged Information by Time Reversal

TL;DR

This paper investigates the fundamental limits of recovering damaged information through time reversal, showing that classical chaos affects recovery quantity but not possibility, and that decoherence imposes an upper bound based on entanglement.

Contribution

It clarifies the origin of information recovery in chaotic systems and quantifies how decoherence constrains the recovery ratio via entanglement measures.

Findings

Classical chaos reduces but does not prevent information recovery.

Decoherence limits recovery, with an upper bound related to entangling power.

Time reversal can partially recover scrambled information despite damage.

Abstract

Recently it was found that scrambled information can be partially recovered by a time-reversed evolution, even after being damaged by an intruder. We reconsider the origin of the information recovery, and argue that the presence of classical chaos does not preclude it and only leads to a quantitative reduction of the recovery ratio. We also show how decoherence (i.e. entanglement with the intruder) limits the recovery, by proving an upper bound on the recovery ratio in terms of the entangling power of the intruder's action.