How Much Entanglement Does a Quantum Code Need?

In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the sender and the receiver have access to pre-shared entanglement. Such codes promise better information rates or improved error handling properties. Entanglement incurs costs and must be judiciously calibrated in designing quantum codes with good performance, relative to their deployment parameters. Revisiting known constructions, we devise tools from classical coding theory to better understand how the amount of entanglement can be varied. We present three new propagation rules and discuss how each of them affects the error handling. Tables listing the parameters of the best performing qubit and qutrit EAQECCs that we can explicitly construct are supplied for reference and comparison.