We provide a procedure to construct entanglement-assisted Calderbank-Shor-Steane (CSS) codes over qudits from the parity check matrices of two classical codes over F _q , where q = p ^k , p is prime, and k is a positive integer. The construction procedure involves the proposed Euclidean Gram-Schmidt orthogonalization algorithm, followed by a procedure to extend the quantum operators to obtain stabilizers of the code. Using this construction, we provide a construction of entanglement-assisted tensor product codes from classical tensor product codes over F _q . We further show that a nonzero rate entanglement-assisted tensor product code can be obtained from a classical tensor product code whose component codes yield zero rate entanglement-assisted CSS codes. We view this result as the coding analog of superadditivity.

For more about this transaction see link below. 

https://ieeexplore.ieee.org/document/9207971

Published in: IEEE Transactions on Quantum Engineering ( Volume: 1)