Towards Two Bloch Sphere Representation of Pure Two-Qubit States and Unitaries.

We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative direction of the coordinate axes of the two Bloch spheres may be used to describe the states. Moreover, the coordinate axes of one Bloch sphere should be rignt-handed and those of the other one should be left-handed. We describe and depict separable and maximally entangled states as well as entangling and non-entangling rotations. We also offer a graphical representation of the workings of a CNOT gate for different inputs. Finally, we provide a way to also represent partially entangled states and describe entanglement measures related to the surface area of the sphere enclosing the state representation.

Crystal structure refinement, low- and high-temperature X-ray diffraction and Mössbauer spectroscopy study of the oxoborate ludwigite from the Iten'yurginskoe deposit.

This paper reports an investigation of the chemistry, crystal structure refinement and thermal behavior (80-1650 K) of ludwigite from the Iten'yurginskoe deposit (Eastern Chukotka, Russia). Its chemical composition was determined by electron microprobe analysis, giving an empirical formula (Mg1.70Fe2+0.29Mn0.01)Σ2.00(Fe3+0.90Al0.08Mg0.02)Σ1.00O2(BO3). A refinement of the crystal structure from single-crystal X-ray diffraction data (SCXRD) was provided for the first time for ludwigite from this deposit (R = 0.047). The structure can be described as a framework composed of [MO6]n- octahedra and isolated [BO3]3- triangles located in triangular interstices of the framework. Based on a comprehensive analysis of SCXRD and Mössbauer spectroscopy data, the M1 site is occupied by Mg, M2 and M3 by Mg and Fe2+, M4 by Fe3+, Mg and Al. There are also oxo-centered [O4M4]n+ and [O2M5]n+ polyhedra building up a framework with the [BO3]3- triangles located in its hexagonal interstices. No indications of magnetic ordering are found in the temperature range investigated. The Fe2+ → Fe3+ oxidation occurs above 600 K, and is accompanied by a decrease of the unit-cell parameters and subsequent incomplete solid-phase decomposition with the formation of hematite, warwickite and magnetite. The mineral melts at temperatures above 1582 K. The thermal expansion of ludwigite is slightly anisotropic, which is explained by a dense packing of the [MO6]n- octahedra as well as a virtually perpendicular orientation of the oxo-centered double chains to each other. At room temperature, maximum expansion is along the c axis (αc = 9.1 × 10-6 K-1) and minimum expansion is in the ab plane (αa = 8.6 × 10-6, αb = 7.6 × 10-6 K-1), which is due to the preferred orientation of the [BO3]3- triangles. A comparison of the thermal behavior of three oxoborates of the ludwigite group, namely azoproite (Mg,Fe2+)2(Fe3+,Ti,Mg,Al)O2(BO3), vonsenite (Fe2+,Mg)2(Fe3+,Mn2+,Sn,Al)O2(BO3) and ludwigite (Mg,Fe2+,Mn)2(Fe3+,Al,Mg)O2(BO3), is provided.

Unitarity of Decoherence Implies Possibility of Decoherence-like Dynamics towards Macroscopic Superpositions.

Quantum decoherence is crucial to understanding the emergence of the classical world from the underlying quantum reality. Decoherence dynamics are unitary, although they superselect a preferred eigenbasis. Decoherence dynamics result in stable macroscopic, localized, classical-like states. We show that the above-mentioned facts imply the possibility of the existence of decoherence-like dynamics that result in stable macroscopic non-localized non-classical-like states. Being rooted in the fabric of the decoherence theory itself, this property implies environments that steer the decoherence towards, for example, spatial superpositions of macroscopic objects. To demonstrate this, we provide thought-experimental, mathematical and philosophical arguments.

Investigation of thermal behavior of mixed-valent iron borates vonsenite and hulsite containing [OM4]n+ and [OM5]n+ oxocentred polyhedra by in situ high-temperature Mössbauer spectroscopy, X-ray diffraction and thermal analysis.

The investigation of elemental composition, crystal structure and thermal behavior of vonsenite and hulsite from the Titovskoe boron deposit in Russia is reported. The structures of the borates are described in terms of cation-centered and oxocentred polyhedra. There are different sequences of double chains and layers consisting of oxocentred [OM4]n+ tetrahedra and [OM5]n+ tetragonal pyramids forming a framework. Elemental composition was determined by energy-dispersive X-ray spectroscopy (EDX). Oxidation states and coordination sites of iron and tin in the oxoborates are determined using Mössbauer spectroscopy and compared with EDX and X-ray diffraction data (XRD). According to results obtained from high-temperature Mössbauer spectroscopy, the Fe2+ to Fe3+ oxidation in vonsenite and hulsite occurs at approximately 500 and 600 K, respectively. According to the high-temperature XRD data, this process is accompanied by an assumed deformation of crystal structures and subsequent solid-phase decomposition to hematite and warwickite. It is seen as a monotonic decrease of volume thermal expansion coefficients with an increase in temperature. A partial magnetic ordering in hulsite is observed for the first time with Tc ≃ 383 K. Near this temperature, an unusual change of thermal expansion coefficients is revealed. Vonsenite starts to melt at 1571 K and hulsite melts at 1504 K. Eigenvalues of thermal expansion tensor are calculated for the oxoborates as well as anisotropy of the expansion is described in comparison with their crystal structures.

The novel borate Lu5Ba6B9O27 with a new structure type: synthesis, disordered crystal structure and negative linear thermal expansion.

Single crystals of Lu5Ba6B9O27 were obtained by cooling from a melt and polycrystals of the borate were prepared using a multi-step solid-state synthesis. The crystal structure was determined from single-crystal X-ray diffraction data. The borate crystallizes in a new structure type in the monoclinic crystal system in space group C2/c, with cell parameters a = 13.0927 (3), b = 9.9970 (2) and c = 20.4884 (4) Å, ß = 106.827 (1)°, V = 2566.86 (9) Å3 and Z = 4. It is described as a framework composed of rings consisting of vertex-sharing [BO3] triangles and [LuO6] octahedra. The Ba atoms are in the cavities of the framework. The structure is disordered: one of the B atoms is surrounded by six O atoms with partial occupancies of 0.5. The thermal properties of Lu5Ba6B9O27 were investigated by thermal analysis and high-temperature X-ray powder diffraction. Its thermal expansion is highly anisotropic. The negative expansion (contraction) is along the b axis, i.e. parallel to the planes of the largest number of [BO3] triangles. The coefficient of negative linear expansion ranges from -1.42 (at 20°C) to -5.57 × 10-6 °C-1 (at 1000°C). Thermal deformation of the ac plane is described in terms of the theory of shear deformation of monoclinic crystals. The Lu5Ba6B9O27 sample melts at 1170°C.

Synthesis and Characterization of the High-Pressure Nickel Borate γ-NiB4O7.

γ-NiB4O7 was synthesized in a high-pressure/high-temperature experiment at 5 GPa and 900 °C. The single-crystal structure analysis yielded the following results: space group P6522 (No. 179), a = 425.6(2), c = 3490.5(2) pm, V = 0.5475(2) nm3, Z = 6, and Flack parameter x = -0.010(5). Second harmonic generation measurements confirmed the acentric crystal structure. Furthermore, γ-NiB4O7 was characterized via vibrational as well as single-crystal electronic absorption spectroscopy, magnetic measurements, high-temperature X-ray diffraction, differential scanning calorimetry, and thermogravimetry. Density functional theory-based calculations were performed to facilitate band assignments to vibrational modes and to evaluate the elastic properties and phase stability of γ-NiB4O7.

Incommensurate modulation and thermal expansion of Sr3B(2†+†x)Si(1†-†x)O(8†-†x/2) solid solutions.

Crystal structures of Sr3B(2 + x)Si(1 - x)O(8 - x/2) solid solutions with nominal compositions x = 0.28, 0.53, 0.78 in the Sr3B2SiO8-Sr2B2O5 section of the SrO-B2O3-SiO2 system are refined using single-crystal X-ray diffraction data. Incommensurate structure modulations are mainly associated with various orientations of corner-sharing (B,Si)-polyhedra. Preference is given to the (3 + 2)-dimensional symmetry group Pnma(0ßγ)000(0ßγ)000 for a single crystal compared with an alternate model of a twin formed by monoclinic components, each of them corresponding to the (3 + 1)-dimensional symmetry group P2(1)/n(0ßγ). Single-phase polycrystalline samples of solid solutions are investigated by high-temperature X-ray powder diffraction in air. Orientation preferences of the BO3 units lead to a strong anisotropy of thermal expansion. Negative expansion is observed along the a axis over the temperature range 303-753 K. Anisotropy decreases both on heating and decreasing of the boron content.