<p>Semiquantum key distribution (SQKD) enables two remote users to establish a confidential key, even against an adversary with unbounded computational power. In an SQKD protocol, one user is called classical user who is restricted to preparing and measuring quantum states in the computational basis. Recently, a novel and interesting reflection-based semiquantum key distribution (RB-SQKD) protocol was proposed, where the classical user’s reflection operations directly contribute to key generation. Security and efficiency are two critical criteria for evaluating SQKD protocols. Standard quantum key distribution (QKD) and SQKD protocols check security by sacrificing raw key resources, typically consuming either half of the raw key or half of the rounds, including potential key-generating rounds. In contrast, the original RB-SQKD protocol performs security checks only on the non-key-generating rounds, resulting in a distinct trade-off between security and efficiency. To unify the security-check mechanism with those of standard QKD and SQKD protocols, this paper proposes two modified RB-SQKD protocols, Protocol&#xa0;1 and Protocol&#xa0;2, wherein half of the rounds are randomly selected for security checks, including potential key-generating rounds. Despite sacrificing half of the raw key bits for testing, both protocols maintain an efficiency above <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(50\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>50</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the original: Protocol&#xa0;1 attains <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\frac{2}{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </math></EquationSource> </InlineEquation> of the original protocol’s efficiency, while Protocol&#xa0;2 preserves the original efficiency. Specifically, Protocol&#xa0;1 introduces two key modifications: optimizing the classical user’s random operation probabilities and eliminating all auxiliary quantum states. Meanwhile, Protocol&#xa0;2 enhances efficiency by reusing previously non-key-generating rounds for key generation. These modifications yield substantial efficiency improvements. In addition, this paper provides rigorous correctness and unconditional security proofs for both protocols and calculates the maximum tolerable error rate under the depolarizing channel assumption. The results offer practical guidance for the design of efficient SQKD protocols, highlighting two promising directions: optimizing the classical user’s random operations and exploiting underutilized quantum resources.</p>

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Reflection-based semiquantum key distribution protocols using half of raw key bits for security checks

  • Wenchen Tan,
  • Xiangfu Zou,
  • Xinting Su,
  • Minghui Cai

摘要

Semiquantum key distribution (SQKD) enables two remote users to establish a confidential key, even against an adversary with unbounded computational power. In an SQKD protocol, one user is called classical user who is restricted to preparing and measuring quantum states in the computational basis. Recently, a novel and interesting reflection-based semiquantum key distribution (RB-SQKD) protocol was proposed, where the classical user’s reflection operations directly contribute to key generation. Security and efficiency are two critical criteria for evaluating SQKD protocols. Standard quantum key distribution (QKD) and SQKD protocols check security by sacrificing raw key resources, typically consuming either half of the raw key or half of the rounds, including potential key-generating rounds. In contrast, the original RB-SQKD protocol performs security checks only on the non-key-generating rounds, resulting in a distinct trade-off between security and efficiency. To unify the security-check mechanism with those of standard QKD and SQKD protocols, this paper proposes two modified RB-SQKD protocols, Protocol 1 and Protocol 2, wherein half of the rounds are randomly selected for security checks, including potential key-generating rounds. Despite sacrificing half of the raw key bits for testing, both protocols maintain an efficiency above \(50\%\) 50 % of the original: Protocol 1 attains \(\frac{2}{3}\) 2 3 of the original protocol’s efficiency, while Protocol 2 preserves the original efficiency. Specifically, Protocol 1 introduces two key modifications: optimizing the classical user’s random operation probabilities and eliminating all auxiliary quantum states. Meanwhile, Protocol 2 enhances efficiency by reusing previously non-key-generating rounds for key generation. These modifications yield substantial efficiency improvements. In addition, this paper provides rigorous correctness and unconditional security proofs for both protocols and calculates the maximum tolerable error rate under the depolarizing channel assumption. The results offer practical guidance for the design of efficient SQKD protocols, highlighting two promising directions: optimizing the classical user’s random operations and exploiting underutilized quantum resources.