Ching-Yi Lai, Todd A. Brun
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 these codes. We consider two di?erent versions of this problem. We ?rst show that any (nondegenerate) standard stabilizer code can be transformed into an EAQEC code that can correct errors on the qubits of both 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 a second scheme, the receiver uses a standard stabilizer code to protect the ebits, which we call a \combination code." The performances of di?erent quantum codes are compared in terms of the channel ?delity over the depolarizing channel. We give a formula for the channel ?delity over the depolarizing channel (or any Pauli error channel), and show that it can be e?ciently approximated by a Monte Carlo calculation. Finally, we discuss the tradeo? between performing extra entanglement distillation and applying an EAQEC code with imperfect ebits.
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http://arxiv.org/abs/1204.0302
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