Bounds on the minimum distance of entanglement-assisted quantum codes

The tables below list parameters

[[n, k, d_lower-d_upper; c]]_q

of entanglement-assisted codes (EAQECC).

q: local dimension of the qudits
n: number of qudits
k: number of encoded/logical qudits
d_lower: lower bound on the minimum distance
d_upper: upper bound on the minimum distance
c: number of required maximally entangled pairs of qudits (non-catalytic setting)

Note: In the catalytic setting, the existence of a code [[n, k, d; c]]_q with c ≥ k > 1 implies the existence of a code [[n, k-1, d; c-1]]_q. We do not consider this case here.

Tables:

qubit codes
qutrit codes

References:

Gaojun Luo, Martianus Frederic Ezerman, Markus Grassl, and San Ling,
"How Much Entanglement Does a Quantum Code Need?",
preprint arXiv:2207.05647 [quant-ph], 13.07.2022.
Markus Grassl,
"Entanglement-assisted quantum communication beating the quantum Singleton bound",
Physical Review A, vol. 103, no. 2, February 2021, L020601.
DOI: 10.1103/PhysRevA.103.L020601 (open access)
Preprint arXiv:2007.01249 [quant-ph]

This page is maintained by Markus Grassl (codes@codetables.de). Last change: 2022-08-16