Entanglement-Assisted Quantum Error-Correcting Codes over Local Frobenius Rings
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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 derive a formula for the minimum number of entanglement qudits required to construct an EAQECC from a linear code over the ring ℤ_p^s. This is used to obtain an exact expression for the minimum number of entanglement qudits required to construct an EAQECC from an additive code over a Galois ring, which significantly extends known results for EAQECCs over finite fields.
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