Entanglement-Assisted Quantum Error-Correcting Codes over Local Frobenius Rings

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. We give a formula for the minimum number of entanglement qudits required to construct an EAQECC from an additive code over a finite Galois ring. This significantly extends known results for EAQECCs over finite fields.