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First-principles calculations are performed to simulate the tetragonal multiferroic material PbVO under uniaxial pressure. A first-order tetragonal to cubic structural phase transition takes place under uniaxial pressure of 1.2 GPa, which is accompanied by abruptly changes of the structural parameters, lattice volume, and atomic displacements. Comparative electronic structure calculations are performed for PbVO with the generalised gradient approximation (GGA) and the B3LYP hybrid functional. The hybrid functional drastically improves the band gap of the ground state of PbVO. The GGA and the B3LYP hybrid functional predict contradictory electronic structures for the high pressure cubic phase of PbVO. The results of the B3LYP hybrid functional calculation disprove the metallisation of PbVO under uniaxial pressure. The insulating electronic structure reproduced with B3LYP is consistent with recent experimental observations of semiconducting behaviour for the high pressure cubic phase of PbVO. [ABSTRACT FROM AUTHOR]

The quantum no-cloning theorem and no-deleting theorem may be the most important quantum features for quantum communications or quantum computations. In this paper, we concentrate typical properties of random quantum evolution. We obtain that universal random evolutions change the generic unknown pure states into their orthogonal states approximately. Moreover, typical random evolutions distort the von Neumann entropy with constants. These results are extended to mixed states with a stronger orthogonal preparation ability. These typical characters are very important for quantum information retrieving or various quantum tasks. [ABSTRACT FROM AUTHOR]

This paper is to investigate the rational approximation of the unitary groups. Specially, based on the Household decomposition we prove that the rational unitary subgroup is dense in the complex unitary group. Moreover, its random approximate property is characterized by the natural Harr measure, which can be used to obtain random unitary matrix. Our simulation shows that these results may be applied to approximate quantum computations. [ABSTRACT FROM AUTHOR]

Quantum one-way functions play a fundamental role in cryptography because of its necessity for the secure encryption schemes taking into account the quantum computer. In this paper our purpose is to establish a theoretical framework for a candidate of the quantum one-way functions and quantum trapdoor functions based on one-parameter unitary groups. The dynamics of parameterized unitary groups ensure the one-wayness and quantum undistinguishability in different levels, and the physical feasibility are derived from the simultaneous approximation of its infinitesimal generators. Moreover, these special functions are used to construct new cryptosystems-the quantum public-key cryptosystems for encrypting both the classical and quantum information. [ABSTRACT FROM AUTHOR]