2025/06/05 by Jorge R. Bolaños-Servín, Bolaños-Servín, Jorge R., Yuriko Pitones +3
Computer Science · Physics and Astronomy · #15A63 #81P55 #94B60 #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 81P70 #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Secondary: 15A63
paper · pdf · doi:10.48550/arxiv.2506.04530
openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.