Coding Analog of Superadditivity Using Entanglement-Assisted Quantum Tensor Product Codes Over Fpk

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 Fq, where q = pk, p is prime, andis 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  Fq. 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]


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