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arXiv:1010.4233 · Physical Review A

Reply to “Comment on ‘Semiquantum-key distribution using less than four quantum states’ ”

Xiangfu Zou, Daowen Qiu

Published Apr 11, 2011• 23 citations
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Abstract

In the preceding Comment [Phys. Rev. A 83, 046301 (2011)], Boyer and Mor pointed out that the first conclusion of Lemma 1 in our paper [X. Zou, D. Qiu, L. Li, L. Wu, and L. Li, Phys. Rev. A 79, 052312 (2009)] is not correct, and therefore, the proof of Theorem 5 based on Lemma 1 is wrong. Furthermore, they gave a direct proof for Theorem 5 and affirmed the conclusions in our original paper. In this Reply, we admit the first conclusion of Lemma 1 is not correct, but we need to point out that the second conclusion of Lemma 1 is correct. Accordingly, all the proofs for Lemma 2, Lemma 3, and Theorems 3--6 are based only on the second conclusion of Lemma 1 and therefore are correct.

DOI
10.1103/physreva.83.046302

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Comment on “Semiquantum-key distribution using less than four quantum states”

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For several decades it was believed that information-secure key distribution requires both the sender and receiver to have the ability to generate and/or manipulate quantum states. Earlier, we showed that quantum key distribution in which one party is classical is possible [Boyer, Kenigsberg, and Mor, Phys. Rev. Lett. 99, 140501 (2007)]. A surprising and very nice extension of that result was suggested by Zou, Qiu, Li, Wu, and Li [Phys. Rev. A 79, 052312 (2009)]. Their paper suggests that it is sufficient for the originator of the states (the person holding the quantum technology) to generate just one state. The resulting semiquantum key distribution, which we call here ``quantum key distribution with classical Alice'' is indeed completely robust against eavesdropping. However, their proof (that no eavesdropper can get information without being possibly detected) is faulty. We provide here a fully detailed and direct proof of their very important result.

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Recently, Zhang, Li, and Guo have proposed a particular eavesdropping attack [Phys. Rev. A {\bf 63}, 036301 (2001), quant-ph/0009042] which shows that my quantum key distribution protocol based on entanglement swapping [Phys. Rev. A {\bf 61}, 052312 (2000), quant-ph/9911025] is insecure. However, security against this attack can be attained with a simple modification. In addition, a simpler version of the protocol using four qubits is introduced.

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Ivo Pietro Degiovanni, Ivano Ruo Berchera, Stefania Castelletto +4 more

In this Reply we propose a modified security proof of the quantum dense key distribution protocol, detecting also the eavesdropping attack proposed by W\'ojcik in his Comment [W\'ojcik, Phys. Rev. A 71, 016301 (2005)].

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In the preceding Comment [Phys. Rev. A 83, 046301 (2011)], Boyer and Mor pointed out that the first conclusion of Lemma 1 in our paper [X. Zou, D. Qiu, L. Li, L. Wu, and L. Li, Phys. Rev. A 79, 052312 (2009)] is not correct, and therefore, the proof of Theorem 5 based on Lemma 1 is wrong. Furthermore, they gave a direct proof for Theorem 5 and affirmed the conclusions in our original paper. In this Reply, we admit the first conclusion of Lemma 1 is not correct, but we need to point out that the second conclusion of Lemma 1 is correct. Accordingly, all the proofs for Lemma 2, Lemma 3, and Theorems 3--6 are based only on the second conclusion of Lemma 1 and therefore are correct.
For several decades it was believed that information-secure key distribution requires both the sender and receiver to have the ability to generate and/or manipulate quantum states. Earlier, we showed that quantum key distribution in which one party is classical is possible [Boyer, Kenigsberg, and Mor, Phys. Rev. Lett. 99, 140501 (2007)]. A surprising and very nice extension of that result was suggested by Zou, Qiu, Li, Wu, and Li [Phys. Rev. A 79, 052312 (2009)]. Their paper suggests that it is sufficient for the originator of the states (the person holding the quantum technology) to generate just one state. The resulting semiquantum key distribution, which we call here ``quantum key distribution with classical Alice'' is indeed completely robust against eavesdropping. However, their proof (that no eavesdropper can get information without being possibly detected) is faulty. We provide here a fully detailed and direct proof of their very important result.
In the preceding Comment it has been claimed that an entangled-based quantum key distribution protocol proposed by Zhang, Li, and Gao [Phys. Rev. A 64, 024302 (2001)] and its generalization to ddd-level systems by Karimipour, Bahraminasab, and Bagherinezhad [Phys. Rev. A 65, 052331 (2002)] are insecure against an attack devised by the authors of the Comment. We invalidate the arguments of the Comment and show that the protocols are still secure.
In reply to the Comment by D. A. Kronberg [Phys. Rev. A 104, 026401 (2021)], we would like to reassure readers that none of the critiques actually apply to our final result of the security analysis, namely, Eq. (30). The major part of the Comment, as well as the conclusions, are derived from the consideration of the multiphoton component, which does not appear in our final result. At the same time, we admit that our original interpretation of multiphoton terms in Eq. (26) as well as the potential extension of Eq. (30) with such terms were not correct. The single-photon component plays an essential role in quantum key distribution and was the only one to appear in the final key rate equation, which is valid against the most general collective attack. The Comment concludes that Eq. (30) ``is incorrect ... and the security proof ... is not complete,'' which, as we show, is not the case.