Perfect Quantum Error-Correcting Condition Revisited

TL;DR

This paper presents a unified approach to quantum error correction using quantum mutual information, clarifies the relationship between subspace and entanglement transmission, and revisits fundamental no-cloning and no-deleting theorems.

Contribution

It introduces a simple, unifying method for perfect quantum error correction based on quantum mutual information and links it to fundamental quantum theorems.

Findings

Equivalence between subspace and entanglement transmission established

Revisits no-cloning and no-deleting theorems in an information-theoretic context

Derives conditions for perfect error correction from fundamental quantum principles

Abstract

A simple and unifying method to show the perfect error-correcting condition is provided based on the quantum mutual information. The one-to-one parameterization of quantum operations and the properties of the quantum relative entropy are used effectively in this paper, where the equivalence between the subspace transmission and the entanglement transmission is clearly presented. We also revisit a variant of the no-cloning and no-deleting theorem based on an information-theoretical tradeoff between two parties for the reversibility of quantum operations, and demonstrate that the no-cloning and no-deleting theorem leads to the perfect error-correcting condition on Kraus operators.