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Physical Review A

Comment on “Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair”

Su‐Juan Qin, Fei Gao, Fen-Zhuo Guo, Qiaoyan Wen

Published Sep 8, 2010• 40 citations
Publisher

Abstract

Three protocols of quantum cryptography with a nonmaximally entangled qubit pair [Phys. Rev. A 80, 022323 (2009)] were recently proposed by Shimizu, Tamaki, and Fukasaka. The security of these protocols is based on the quantum-mechanical constraint for a state transformation between nonmaximally entangled states. However, we find that the second protocol is vulnerable under the correlation-elicitation attack. An eavesdropper can obtain the encoded bit $M$ although she has no knowledge about the random bit $R$.

DOI
10.1103/physreva.82.036301

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Three protocols of quantum cryptography with a nonmaximally entangled qubit pair [Phys. Rev. A 80, 022323 (2009)] were recently proposed by Shimizu, Tamaki, and Fukasaka. The security of these protocols is based on the quantum-mechanical constraint for a state transformation between nonmaximally entangled states. However, we find that the second protocol is vulnerable under the correlation-elicitation attack. An eavesdropper can obtain the encoded bit MMM although she has no knowledge about the random bit RRR.
The security of the second (STF-B) protocol of quantum cryptography proposed by Shimizu, Tamaki and Fukasaka (STF) [Phys. Rev. A80 (2009) 022323] is analyzed in a general way, which shows that the STF-B protocol is vulnerable under a kind of generalized attack. Sufficient and necessary condition for which Eve can successfully attack the message M without introducing errors is deduced. It shows that the correlation-elicitation (CE) attack strategy found by Qin et al. [Phys. Rev. A82 (2010) 036301] is a special case of the sufficient and necessary condition. Next, we advance an effective and efficient strategy to prevent the general attack. Hence, the STF-B protocol is revised to a secure one by improving the control mode.
This paper proposes a scheme for quantum cryptography with a nonmaximally entangled qubit pair. In a two-way configuration similar to quantum super dense coding, a two-bit key can be distributed by a round trip of one particle of the qubit pair and received by an appropriate joint measurement with the other. The security of our scheme is based on the quantum-mechanical impossibility of local unitary transformation between certain nonmaximally entangled states. Although an eavesdropper, Eve, can always identify the quantum state and intercept the key, it is impossible for her to resend the state with a unity probability and the legitimate parties inevitably detect her. Our protocol is also capable to quantum secure direct communication.
Entanglement-measurement attack is one of the most famous attacks against quantum cryptography. In quantum cryptography protocols, eavesdropping checking is an effective means to resist this attack. There are currently two commonly used eavesdropping checking methods: one is to prepare two sets of non-orthogonal single-particle states as decoy states, and determine whether there are eavesdroppers in the quantum channel by comparing the states obtained by measurements with the original states; The other is to prepare two sets of non-orthogonal entangled states and use their entanglement correlations to judge whether there are eavesdroppers in the quantum channel. In this paper, we theoretically demonstrate how quantum cryptography can utilize these two eavesdropping checking methods to resist entanglement-measurement attacks. We take the quantum cryptography protocols based on maximally entangled states as examples to demonstrate the proof process, transitioning from qubit-based protocols to qudit-based ones.
The authors call attention to previous work with related result, a quantum-key-distribution scheme based on partial unknown entanglement with Wigner's inequality to establish the security of the quantum channel. The sender chooses any entangled state from a certain set or its equivalent state randomly, and sends a sequence of particles out of each pair to the receiver. The two users each choose between two measurements along the fixed axes. In fact, this is a quantum cryptosystem based on mixed entanglement. The main paper was published in Phys. Rev. A 64, 032305 (2001).
Recently, a ``counterfactual'' quantum-key-distribution scheme was proposed by T.-G. Noh [Phys. Rev. Lett. 103, 230501 (2009)]. In this scheme, two legitimate distant peers may share secret keys even when the information carriers are not traveled in the quantum channel. We find that this protocol is equivalent to an entanglement distillation protocol. According to this equivalence, a strict security proof and the asymptotic key bit rate are both obtained when a perfect single-photon source is applied and a Trojan horse attack can be detected. We also find that the security of this scheme is strongly related to not only the bit error rate but also the yields of photons. And our security proof may shed light on the security of other two-way protocols.