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Performance of entanglement-assisted quantum codes with noisy ebits over asymmetric and memory channels |
| Ji-Hao Fan(樊继豪)†, Pei-Wen Xia(夏沛文), Di-Kang Dai(戴迪康), and Yi-Xiao Chen(陈一骁) |
| School of Cyber Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China |
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Abstract Entanglement-assisted quantum error correction codes (EAQECCs) play an important role in quantum communications with noise. Such a scheme can use arbitrary classical linear code to transmit qubits over noisy quantum channels by consuming some ebits between the sender (Alice) and the receiver (Bob). It is usually assumed that the preshared ebits of Bob are error free. However, noise on these ebits is unavoidable in many cases. In this work, we evaluate the performance of EAQECCs with noisy ebits over asymmetric quantum channels and quantum channels with memory by computing the exact entanglement fidelity of several EAQECCs. We consider asymmetric errors in both qubits and ebits and show that the performance of EAQECCs in entanglement fidelity gets improved for qubits and ebits over asymmetric channels. In quantum memory channels, we compute the entanglement fidelity of several EAQECCs over Markovian quantum memory channels and show that the performance of EAQECCs is lowered down by the channel memory. Furthermore, we show that the performance of EAQECCs is diverse when the error probabilities of qubits and ebits are different. In both asymmetric and memory quantum channels, we show that the performance of EAQECCs is improved largely when the error probability of ebits is reasonably smaller than that of qubits.
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Received: 25 May 2023
Revised: 28 August 2023
Accepted manuscript online: 29 August 2023
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PACS:
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03.67.Lx
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(Quantum computation architectures and implementations)
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03.67.Pp
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(Quantum error correction and other methods for protection against decoherence)
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| Fund: Project supported by the National Key R&D Program of China (Grant No.2022YFB3103802), the National Natural Science Foundation of China (Grant Nos.62371240 and 61802175), and the Fundamental Research Funds for the Central Universities (Grant No.30923011014). |
Corresponding Authors:
Ji-Hao Fan
E-mail: jihao.fan@outlook.com
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Cite this article:
Ji-Hao Fan(樊继豪), Pei-Wen Xia(夏沛文), Di-Kang Dai(戴迪康), and Yi-Xiao Chen(陈一骁) Performance of entanglement-assisted quantum codes with noisy ebits over asymmetric and memory channels 2023 Chin. Phys. B 32 120304
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