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International Journal of Theoretical Physics

Improved Quantum “Ping-Pong” Protocol Based on Five-Qubit GHZ State and Classical CNOT Operation

Jian Li, Danjie Song, Xiao-Jing Guo, Bo Jing

Published Aug 18, 2011• 0 citations
Publisher
DOI
10.1007/s10773-011-0906-8

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This work presents an analysis of a sequential passive eavesdropping attack by two eavesdroppers on the ping-pong protocol employing three-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states. An analytical expression is derived for the probability of attack detection by legitimate users. It is shown that increasing the number of eavesdroppers in the quantum channel leads to a higher probability of attack detection. Expressions are also obtained for the maximum amount of information that two eavesdroppers can gain during their sequential passive attack. The analysis demonstrates that the ping-pong protocol with GHZ triplets is no more vulnerable to passive eavesdropping by two adversaries than it is to an attack by a single one. The results can be generalized to ping-pong protocols based on n-qubit GHZ states for arbitrary values of n\boldsymbol{n}n.
Abstract We analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulnerability towards eavesdropping. On the other hand, partially entangled nonorthogonal basis set holds importance for transferring two-bit information, one each from a sender, to a single receiver. The protocol is further analysed for various eavesdropping attacks, and the results are compared with the use of two shared Bell pairs for two-bit information transfer. Surprisingly, the use of partially entangled nonorthogonal set of states is found to offer better qubit efficiency and increased security, as against the use of two separate maximally entangled Bell states with orthogonal basis. In addition, we also propose a mixed-state sharing protocol to further enhance the security of the PP protocol.