Quantum error-correcting codes via inner products and error bases
Quantum Physics
2025-06-06 v1 Mathematical Physics
math.MP
Abstract
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error (or noise) bases defined on corrupting subspaces. This viewpoint yields new necessary and sufficient conditions for the existence of quantum error-correcting codes in terms of these inner products. The obtained results extend the foundations of quantum error correction beyond classical analogies, highlighting the structural insights offered by operator theory and the underlying product space.
Cite
@article{arxiv.2506.04530,
title = {Quantum error-correcting codes via inner products and error bases},
author = {Jorge R. Bolaños-Servín and Yuriko Pitones and Josué I. Rios-Cangas},
journal= {arXiv preprint arXiv:2506.04530},
year = {2025}
}
Comments
20 pages