Approximate Quantum Error Correction via Complementary Observables

TL;DR

This paper introduces new conditions for approximate quantum error correction based on the predictability of complementary observables, linking entanglement recovery to classical information about quantum states.

Contribution

It presents two novel conditions for approximate quantum error correction using the concept of complementary observables and their predictability.

Findings

Entanglement is recoverable when one system predicts two complementary observables.

Entanglement is recoverable when the environment cannot predict either observable.

New conditions connect classical predictability with quantum error correction.

Abstract

The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be used to construct two new conditions for approximate quantum error correction. The first states that entanglement is locally recoverable from a bipartite state when one system can be used to approximately predict the outcomes of two complementary observables on the other. The second, more in the spirit of the recent decoupling approach, states that entanglement is locally recoverable when the environment cannot reliably predict either.