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Chinese Physics B

Quantum secure direct communication with Greenberger–Horne–Zeilinger-type state (GHZ state) over noisy channels

Zhang Xiaolong, Yuexia Zhang, Wei Hua

Published Feb 1, 2009• 14 citations
Publisher

Abstract

We propose a quantum error-rejection scheme for direct communication with three-qubit quantum codes based on the direct communication of secret messages without any secret key shared in advance. Given the symmetric and independent errors of the transmitted qubits, our scheme can tolerate a bit of error rate up to 33.1%, thus the protocol is deterministically secure against any eavesdropping attack even in a noisy channel.

DOI
10.1088/1674-1056/18/2/010

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We propose a quantum error-rejection scheme for direct communication with three-qubit quantum codes based on the direct communication of secret messages without any secret key shared in advance. Given the symmetric and independent errors of the transmitted qubits, our scheme can tolerate a bit of error rate up to 33.1%, thus the protocol is deterministically secure against any eavesdropping attack even in a noisy channel.
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The direct communication protocol of quantum network over noisy channel is proposed and investigated in this study. In communication process, all quantum nodes share multiparticle Greenberger-Horne-Zeilinger (GHZ)-states. The sending node takes the GHZ-state particle in the hand as the control qubit and the particle for sending secret information as the target qubit, which carries out the CNOT gate operation for the control and target qubit. Each receiving node takes the GHZ-state particle in the hand as the control qubit and the particle of the received secret information as the target qubit, in which the CNOT gate operation is repeated to obtain the secret information that contains the bit error. Each receiving node uses the extracted part of qubits as the checking qubits, and then corrects the bit-flip errors using parity check matrix together with the rest part of qubits. As a result, all receiving nodes obtain rectified secret information. In addition to the high security analysis, this study also presents the detailed analyses of the throughput efficiency and the communication performance.
In this paper, we present an (n, n) threshold quantum secret sharing scheme of secure direct communication using Greenberger-Horne-Zeilinger state. The present scheme is efficient in that all the Greenberger-Horne-Zeilinger states used in the quantum secret sharing scheme are used to generate shared secret messages except those chosen for checking eavesdropper. In our scheme, the measuring basis of communication parties is invariable and the classical information used to check eavesdropping needs only the results of measurements of the communication parties. Another nice feature of our scheme is that the sender transmit her secret messages to the receivers directly and the receivers recover the sender's secret by combining their results, different from the QSS scheme whose object is essentially to allow a sender to establish a shared key with the receivers. This feature of our scheme is similar to that of quantum secret direct communication.
The notion of quantum secure direct communication(QSDC)has been introduced recently in quantum as a supplement for quantum key distribution,in which Alice and Bob exchange messages secure classical message without establishing any shared keys previously.Differ from quantum key distribution,as a kind of deterministic communication,QSDC is more easily affected by the noisy channel,in this case we need stronger error correction method in QSDC.In this paper,aquantum secure direct communication protocol using GHZ state based on stabiliser codes theory is presented.Our protocol can not only maintain unconditional security,but also find and correct one quantum bit phase error,efficiently diminish the quantum bit error rate in noisy channel.
A protocol for three-party quantum secure direct communication based on Greenberger–Horne–Zeilinger (GHZ) states was recently proposed by Jin et al. [Phys. Lett. A 354 (2006) 67] By analysing the protocol we find some security loopholes, e.g. one bit of secret messages of a party (Alice in the original paper) can always be leaked straight to the public without any eavesdropping. These problems suggested previously are discussed and possible solutions are presented to improve the security of the original protocol.