As a new model for signing quantum message, arbitrated quantum signature (AQS) has recently received a lot of attention. In this paper we study the cryptanalysis of previous AQS protocols from the aspects of forgery and disavowal. We show that in these protocols the receiver Bob can realize existential forgery of the sender's signature under known message attack. Bob can even achieve universal forgery when the protocols are used to sign a classical message. Furthermore, the sender Alice can successfully disavow any of her signatures by simple attack. The attack strategies are described in detail and some discussions about the potential improvements of the protocols are given. Finally we also present several interesting topics in future study on AQS protocols.Comment: 7 pages, no figure

The participant attack is the most serious threat for quantum secret-sharing protocols. We present a method to analyze the security of quantum secret-sharing protocols against this kind of attack taking the scheme of Hillery, Bužek, and Berthiaume (HBB) [Phys. Rev. A 59 1829] as an example. By distinguishing between two mixed states, we derive the necessary and sufficient conditions under which a dishonest participant can attain all the information without introducing any error, which shows that the HBB protocol is insecure against dishonest participants. It is easy to verify that the attack scheme of Karlsson, Koashi, and Imoto [Phys. Rev. A 59, 162 (1999)] is a special example of our results. To demonstrate our results further, we construct an explicit attack scheme according to the necessary and sufficient conditions. Our work completes the security analysis of the HBB protocol, and the method presented may be useful for the analysis of other similar protocols.

The ring-arrangement quantum secret sharing protocol in the paper [K. Br\'{a}dler and M. Du\v{s}ek (2004) {\textit{J. Opt. B: Quantum Semiclass. Opt.}} {\textbf{6}} 63] is analyzed and it is shown that this protocol is secure for any eavesdropper except for a dishonest participant. For example, by a special strategy, Bob can steal Charlie's portion of information without being detected and then recover Alice's secret by himself. We give a description of this strategy and point out a possible way to improve the protocol to stand against this attack.

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The Poisson equation has wide applications in many areas of science and engineering. Although there are some quantum algorithms that can efficiently solve the Poisson equation, they generally require a fault-tolerant quantum computer which is beyond the current technology. In this paper, we propose a Variational Quantum Algorithm (VQA) to solve the Poisson equation, which can be executed on Noise Intermediate-Scale Quantum (NISQ) devices. In detail, we first adopt the finite difference method to transform the Poisson equation into a linear system. Then, according to the special structure of the linear system, we find an explicit tensor product decomposition, with only 2 log n + 1 items, of its coefficient matrix under a specific set of simple operators, where n is the dimension of the coefficient matrix. This implies that the proposed VQA only needs O(log n) measurements, which dramatically reduce quantum resources. Additionally, we perform quantum Bell measurements to efficiently evaluate the expectation values of simple operators. Numerical experiments demonstrate that our algorithm can effectively solve the Poisson equation.