Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 protocol in fully quantum cryptography into SQKD. In this protocol, the sender Alice just sends one quantum state to the classical Bob and Bob just prepares a fixed state in the preparation process. It is much simpler than the existing SQKD and potentially much easier to be implemented. It can be seen as a semi-quantum version of B92 protocol, compared to the protocol BKM07 as the semi-quantum version of BB84 in fully quantum cryptography. We verify that it is more efficient than the existing single-state SQKD protocols by introducing an efficiency parameter. Specifically, we prove it is secure against a restricted collective attack by computing a lower bound of the key rate in the asymptotic scenario. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be definitely established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case the reverse channel is a depolarizing one with parameter [Formula: see text]. Though the threshold value is a little smaller than those of some existing SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.

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单态半量子密钥分发协议及其安全证明

半量子密钥分发 (SQKD) 可以通过使用比其完全量子对应物更少的量子资源来共享密钥，这可能使 SQKD 变得更加实用和可实现。在本文中，我们将全量子密码学中的 B92 协议的思想引入 SQKD，提出了一种新的 SQKD 协议。在这个协议中，发送方 Alice 只向经典 Bob 发送一个量子状态，而 Bob 在准备过程中只准备一个固定状态。它比现有的 SQKD 简单得多，并且可能更容易实现。它可以看作是 B92 协议的半量子版本，而 BKM07 协议是全量子密码学中 BB84 的半量子版本。我们通过引入效率参数来验证它比现有的单态 SQKD 协议更有效。具体来说，我们通过在渐近场景中计算密钥速率的下限来证明它对受限集体攻击是安全的。然后我们可以找到一个错误阈值，使得对于所有小于这个值的错误率，在合法用户之间肯定可以建立安全密钥。我们说明了如何计算阈值，以防反向通道是带有参数的去极化通道[公式：参见文本]。虽然阈值比现有的一些 SQKD 协议的阈值要小一些，但在全量子密码学中可以与 B92 协议相媲美。合法用户之间肯定可以建立安全密钥。我们说明了如何计算阈值，以防反向通道是带有参数的去极化通道[公式：参见文本]。虽然阈值比现有的一些 SQKD 协议的阈值要小一些，但在全量子密码学中可以与 B92 协议相媲美。合法用户之间肯定可以建立安全密钥。我们说明了如何计算阈值，以防反向通道是带有参数的去极化通道[公式：参见文本]。虽然阈值比现有的一些 SQKD 协议的阈值要小一些，但在全量子密码学中可以与 B92 协议相媲美。