A serious problem in cloud computing is privacy information protection. This study proposes a new private comparison protocol using Einstein-Podolsky-Rosen (EPR) pairs. This protocol allows two parties to secretly compare their classical information. Quantum dense coding enables the comparison task to be completed with the help of a classical semi-honest center. A one-step transmission scheme and designed decoy photons can be used against various quantum attacks. The new protocol can ensure fairness, efficiency, and security. The classical semi-honest center cannot learn any information about the private inputs of the players. Moreover, this scheme can be easily generalized using the general EPR pairs in order to improve the transmission efficiency.
Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions of qubit systems, we investigate the possibility of ququart systems (four-dimensional states) dependent on two DOFs of photon systems. We propose some useful one-parameter four-dimensional quantum transformations for the construction of universal ququart logic gates. The interface between the spin of a photon and an electron spin confined in a quantum dot embedded in a microcavity is applied to build universal ququart logic gates on the photon system with two freedoms. Our elementary controlled-ququart gates cost no more than 8 CNOT gates in a qubit system, which is far less than the 104 CNOT gates required for a general four-qubit logic gate. The ququart logic is also used to generate useful hyperentanglements and hyperentanglement-assisted quantum error-correcting code, which may be available in modern physical technology.
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden principles to unify these results. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed state in Hilbert space of a finite dimension. Two general forms include the no-cloning theorem, the no-deleting theorem, and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the input pure states. The generalized upper bounds for the success probability are proved. Third, we generalize a recent superposing of unknown states with fixed overlaps when multiple copies of the input states are available.
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