For quantum communication in a gravitational field, the properties of the Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of general relativity. Acceleration and gravity are shown to deteriorate the perfect anticorrelation of an EPR pair of spins in the same direction, and apparently decrease the degree of the violation of Bell's inequality. To maintain the perfect EPR correlation and the maximal violation of Bell's inequality, observers must measure the spins in appropriately chosen different directions which depend on the velocity of the particles, the curvature of the space-time, and the positions of the observers. Near the event horizon of a black hole, the appropriate directions depend so sensitively on the positions of the observers that even a very small uncertainty in the identification of the observers' positions leads to a fatal error in quantum communication, unless the observers fall into the black hole together with the particles.

A solid solution of zinc oxide and germanium nitride (Zn 1+x Ge)(N 2 O x ) (x ) 0.44) is demonstrated to be an effective photocatalyst for overall water splitting under ultraviolet and visible light. The catalyst is prepared by reaction of GeO 2 and ZnO under ammonia flow (20 mL‚min -1 ) at 1123 K for 15 h. The crystal structure of the material is investigated by a combination of Rietveld analysis and the maximum-entropy method using neutron powder diffraction data. The (Zn 1.44 Ge)(N 2.08 O 0.38 ) catalyst is confirmed to have a wurtzite-type structure (space group P6 3 mc) and to be the solid solution where the oxygen atoms are substituted for nitrogen atoms. The (Zn 1.44 Ge)(N 2.08 O 0.38 ) catalysts thus prepared exhibit a band gap of ca. 2.7 eV and corresponding activity at visible wavelengths. The decrease in band gap compared to the starting materials is attributed to larger valance band dispersion resulting from the energy difference between O2p and N2p orbitals and from the p-d repulsion between Zn3d and N2p+O2p electrons in the upper valance band, which raises the top of the valance band. (Zn 1.44 Ge)(N 2.08 O 0.38 ) powder modified by surface loading with RuO 2 nanoparticles at 5 wt % achieves overall water splitting under both ultraviolet and visible irradiation.

We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction is deteriorated in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing the velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. We must take account of this relativistic effect in utilizing in moving frames the EPR correlation and the violation of Bell's inequality for quantum communication. PACS : 03.67.-a, 03.30.+p, 03.65.Ud, 11.30.Cp, 02.20.-a P |p, σ = p |p, σ , (2.12)where p = (p 1 , p 2 , p 3 ), but that J 3 |p, σ = σh |p, σ .(2.13) This is because J 3 now contains a contribution from the orbital motion. Since we have J 3 , P 1 = ihP 2 = 0,Since the explicit forms of these operators are unnecessary for our present purpose, we simply view Eqs. (A.19) and (A.20) as the definitions of J and K.In order for these unitary operators to represent the Poincaré group, the generators H, P , J, and K must satisfy the commutation relations [11],When K = 0, we obtain the usual commutation relations of ISO(3) which consists of spatial translations and rotations.