Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries

TL;DR

This paper introduces trace-norm isometric encoding for quantum information, providing a foundation for error protection and correction, and analyzing robustness against imperfections and deviations in quantum systems.

Contribution

It establishes the concept of trace-norm isometric encoding, linking quantum codes with error protection, and explores robustness properties under practical imperfections.

Findings

Operational foundation for the subsystems principle

Connections between noiseless, protectable, and correctable codes

Robustness analysis against imperfect initialization and errors

Abstract

We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle" [E. Knill, Phys. Rev. A 74, 042301 (2006)] for faithfully realizing quantum information in physical systems, our approach allows additional explicit connections between noiseless, protectable, and correctable quantum codes to be identified. Robustness properties of isometric encodings against imperfect initialization and/or deviations from the intended error models are also analyzed.