Coding Analog of Superadditivity Using Entanglement-Assisted Quantum Tensor Product Codes Over F_p^k

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.

Faculty Member: Shayan Srinivasa Garani [ESE]

References

• Priya J. Nadkarni and Shayan Srinivas Garani, Coding Analog of Superadditivity Using Entanglement-Assisted Quantum Tensor Product Codes Over F_p^k, in IEEE Trans. on Quantum Engineering, Oct. 2020