2022/02/01 by Tania Sidana, Sidana, Tania, Navin Kashyap +1
Computer Science · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · doi:10.48550/arxiv.2202.00248
openalex publication_date 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this paper, we provide a framework for constructing entanglement-assisted quantum error-correcting codes (EAQECCs) from classical additive codes over a finite commutative local Frobenius ring R. At the heart of the framework, and this is one of the main technical contributions of our paper, is a procedure to construct, for an additive code C over R, a generating set for C that is in standard form, meaning that it consists purely of isotropic generators and hyperbolic pairs. Moreover, when R is a Galois ring, we give an exact expression for the minimum number of pairs of maximally entangled qudits required to construct an EAQECC from an additive code over R, which significantly extends known results for EAQECCs over finite fields. We also demonstrate how adding extra coordinates to an additive code can give us a certain degree of flexibility in determining the parameters of the EAQECCs that result from our construction.