一种有效的量子纠错和身份认证的组合
An efficient combination of quantum error correction and authentication
摘要：
当通过信道发送量子信息时，我们希望确保消息保持完整。量子纠错和量子认证都旨在保护（量子）信息，但从两个非常不同的方向来实现这一任务：纠错码可以防止概率信道噪声，并且对小错误非常鲁棒，而认证码可以防止对抗性攻击，并且对任何错误都非常敏感，包括小错误。实际上，当通过有噪信道发送已验证状态时，必须将其包裹在纠错码中，以平衡底层验证方案的敏感性。我们研究的问题，这是否可以更有效地通过在一个单一的代码中结合这两个功能。为了说明这种组合的潜力，我们设计的阈值代码，修改的陷阱认证码，保留该代码的认证属性，但自然是强大的去极化信道噪声。我们表明，阈值码需要polyacromically更少的量子位，以实现相同水平的安全性和鲁棒性，相比天真的陷阱码与任何级联CSS代码的组成。我们相信，我们的分析打开了大门，结合更一般的纠错码和认证码，这可以提高所产生的计划的实用性。
英文摘要：
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very different directions: error-correcting codes protect against probabilistic channel noise and are meant to be very robust against small errors, while authentication codes prevent adversarial attacks and are designed to be very sensitive against any error, including small ones. In practice, when sending an authenticated state over a noisy channel, one would have to wrap it in an error-correcting code to counterbalance the sensitivity of the underlying authentication scheme. We study the question of whether this can be done more efficiently by combining the two functionalities in a single code. To illustrate the potential of such a combination, we design the threshold code, a modification of the trap authentication code which preserves that code's authentication properties, but which is naturally robust against depolarizing channel noise. We show that the threshold code needs polylogarithmically fewer qubits to achieve the same level of security and robustness, compared to the naive composition of the trap code with any concatenated CSS code. We believe our analysis opens the door to combining more general error-correction and authentication codes, which could improve the practicality of the resulting scheme.
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