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Measure-Resend Semi-Quantum Private Comparison Without Entanglement

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Abstract

In this paper, we successfully design the semi-quantum private comparison (SQPC) protocol with the measure-resend characteristic by using two-particle product states as the initial prepared quantum resource which allows two classical users to compare the equality of their private secrets under the help of a quantum third party (TP). The quantum TP is semi-honest in the sense that he is allowed to misbehave on his own but cannot conspire with either of users. Both the output correctness and the security against the outside attack and the participant attack can be guaranteed. Compared with the previous SQPC protocols, the advantage of our protocol lies in that it only employs two-particle product states as the initial prepared quantum resource, only requires TP to perform single-photon measurements and does not need quantum entanglement swapping. Our protocol can be realized with current quantum technologies.

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Acknowledgments

Funding by the Natural Science Foundation of Zhejiang Province (Grant No.LY18F0 20007) is gratefully acknowledged.

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  1. College of Information & Electronic Engineering, Zhejiang Gongshang University, Hangzhou, 310018, People’s Republic of China

    Tian-Yu Ye & Chong-Qiang Ye

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Appendix

Appendix

Lu and Cai’s three-party circled SQKD protocol:

In Lu and Cai’s three-party circled SQKD protocol, classical Bob and classical Charlie can establish a sequence of random key bits between them with the assistance of a quantum TP. This protocol is described as follows.

In each run, TP always prepares a qubit in σX basis and sends it out through the quantum channel. When a qubit is arriving, both Bob and Charlie can either let it go undisturbed or measure it in σZ basis, prepare a fresh one randomly in σZ basis and send it. TP receives the travel back qubit and measures it in σX basis or σZ basis randomly. There are three possibilities: (p0) Neither Bob nor Charlie disturbed the travel qubit; (p1) One of them measured the travel qubit but the other did not; (p2) Both Bob and Charlie measured the travel qubit.

After all of TP’s qubits have been distributed, Bob, Charlie and TP can publish their operations through their classical channels. When (p0) happened, the travel qubit has not been disturbed so that they can use this run as CTRL if TP has measured it in σX basis. When (p1) happened, Bob or Charlie publishes the state of the travel back qubit and then they can also use this run as CTRL if TP has measured the travel qubit in σZ basis. When (p2) happened, Charlie knows the state Bob prepared so that Bob and Charlie share a common bit as SIFT bit. In the end, Bob and Charlie will publish some of their SIFT bits to verify QBER in SIFT. If both QBER in SIFT and QBER in CTRL are tolerable, Bob and Charlie can use the rest SIFT bits as INFO bits to generate final key bits after error-correction and privacy amplification.

It is necessary to emphasize that TP cannot share Bob and Charlie’s key bits since Charlie refreshes each travel qubit in SIFT.

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Ye, TY., Ye, CQ. Measure-Resend Semi-Quantum Private Comparison Without Entanglement. Int J Theor Phys 57, 3819–3834 (2018). https://doi.org/10.1007/s10773-018-3894-0

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