# Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

## TL;DR

This paper extends the theory of entanglement-assisted quantum error-correcting codes (EAQECCs) to arbitrary finite fields, providing formulas, bounds, and constructions applicable beyond binary fields.

## Contribution

It generalizes existing EAQECC formulas and bounds to all finite fields and introduces new constructions from punctured self-orthogonal codes.

## Key findings

- Optimal entanglement requirements formula extended to all finite fields
- Gilbert-Varshamov bound established for EAQECCs over arbitrary fields
- New constructions from punctured self-orthogonal codes

## Abstract

We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.