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Entanglement-Assisted Quantum Error-Correcting Codes when the Ebits of Receiver are not Perfect

Ching-Yi Lai, University of Southern California

(Session 10b : Saturday from 5:00pm-5:30pm)

Abstract. The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability of quantum codes. We provide two different schemes to cope with this problem. We first show that any (nondegenerate) standard stabilizer codes can be transformed into EAQEC codes that can correct both errors on the qubits of sender and receiver. These EAQEC codes are equivalent to standard stabilizer codes, and hence the decoding techniques of standard stabilizer codes can be applied. Several EAQEC codes of this type are found to be optimal. In the second scheme, the receiver uses a standard stabilizer code to protect the ebits. The decoding procedure has two stages: decode the ebits of the receiver and then decode the information protected by the EAQEC code. To achieve high channel capacity, the second scheme is preferable, with a good EAQEC code that is not equivalent to any standard stabilizer code, at the cost of more resources at the receiver. Several optimal EAQEC codes not equivalent to any standard stabilizer code are found by the encoding optimization algorithm.