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International Journal of Theoretical Physics

A Quantum Single Sign-On Protocol Based on GHZ States

Xingtian Ren, Yong Wang, Guiping Dai

Published Mar 20, 2015• 0 citations
Publisher
DOI
10.1007/s10773-015-2611-5

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Abstract The concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a new kind of logic-qubit entangled state, which may have extensive applications in future quantum communication. In this letter, we propose a protocol for constructing an arbitrary C-GHZ state with single photons. We exploit the cross-Kerr nonlinearity for this purpose. This protocol has some advantages over previous protocols. First, it only requires two kinds of cross-Kerr nonlinearities to generate single phase shifts ± θ . Second, it is not necessary to use sophisticated m -photon Toffoli gates. Third, this protocol is deterministic and can be used to generate an arbitrary C-GHZ state. This protocol may be useful in future quantum information processing based on the C-GHZ state.
Recently, Zheng et al. presented a novel signature protocol with arbitrator based on XOR encryption and GHZ state. Unfortunately, their protocol lacks security. Firstly, a quantum adversary can forge their signature based on the received information. On the other hand, their protocol is vulnerable for the adversary’s repudiation attack. Then, we bring about improvements on its security, efficiency and practicality. The improved protocol not only prevents the security defects of the old protocol, but also has better computation efficiency. On the other hand, our protocol is mainly used to sign the classical messages, which are widely used in the current network.
We present optimized distillation schemes for preparing Greenberger-Horne-Zeilinger (GHZ) states. Our approach relies on training variational quantum circuits with white noise affected GHZ states as inputs. Optimizing for a single iteration of the scheme, we find that it is possible to achieve an increased fidelity to the GHZ state, although further iterations decrease the fidelity. The same scheme, acting on coherently distorted pure-state inputs, is effective only in certain special cases. We show that radically different results can be achieved, however, when one optimizes for the output after two iterations of the protocol. In this case, the obtained schemes are more effective in distilling GHZ states from inputs affected by white noise. Moreover, they can also correct several types of coherent pure-state errors.