On the Limits of Information Retrieval in Quantum Mechanics

TL;DR

This paper explores fundamental limitations in retrieving information from quantum states, highlighting that perfect information recovery is practically impossible due to the nature of quantum evolution and finite-dimensional approximations.

Contribution

It demonstrates that most quantum evolutions can be approximated by finite-rank operators and that exact information retrieval requires infinite time, challenging assumptions about information preservation.

Findings

Most quantum operators can be approximated by finite-rank operators.

Exact information retrieval from nonstationary states is practically impossible within finite time.

Quantum evolution approximations impact the understanding of information preservation.

Abstract

The widely considered assertion is that the unitarity of quantum mechanical evolution assures the preservation of information. It is even promoted in popular literature as an established fact. (Susskind, 2008) Yet, a simple chain of reasoning demonstrates that: 1) almost any evolutionary operator can be well approximated by a degenerate (finite-rank) operator and 2) one needs an eternity to retrieve information exactly from a nonstationary quantum state and to distinguish between arbitrary unitary operator and its finite-dimensional approximations.