Mutually unbiased bases in dimension six: The four most distant bases

We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in dimension six. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically-found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.Comment: 10 pages, 2 figures, 1 tabl

Rotational cooling of trapped polyatomic molecules

Controlling the internal degrees of freedom is a key challenge for applications of cold and ultracold molecules. Here, we demonstrate rotational-state cooling of trapped methyl fluoride molecules (CH3F) by optically pumping the population of 16 M-sublevels in the rotational states J=3,4,5, and 6 into a single level. By combining rotational-state cooling with motional cooling, we increase the relative number of molecules in the state J=4, K=3, M=4 from a few percent to over 70%, thereby generating a translationally cold (~30mK) and nearly pure state ensemble of about 10^6 molecules. Our scheme is extendable to larger sets of initial states, other final states and a variety of molecule species, thus paving the way for internal-state control of ever larger molecules

Анализ социальных медиа

The experimental electron-density distributions in crystals of five chain polymers [M(μ-X)2(py)2] (M = Zn, Cd; X = Cl, Br; py = 3,5-substituted pyridine) have been obtained from high-resolution X-ray diffraction data sets (sin θ/λ > 1.1 Å−1) at 100 K. Topological analyses following Bader's `Atoms in Molecules' approach not only confirmed the existence of (3, −1) critical points for the chemically reasonable and presumably strong covalent and coordinative bonds, but also for four different secondary interactions which are expected to play a role in stabilizing the polymeric structures which are unusual for Zn as the metal center. These weaker contacts comprise intra- and inter-strand C—H⋯X—M hydrogen bonds on the one hand and C—X⋯X—C interhalogen contacts on the other hand. According to the experimental electron-density studies, the non-classical hydrogen bonds are associated with higher electron density in the (3, −1) critical points than the halogen bonds and hence are the dominant interactions both with respect to intra- and inter-chain contacts

Phase-dependent which-way information

We introduce a new observable for reading out a which-way detector in a Young-type interferometer whose eigenstates either contain full which-way information or none at all. We calculate the which-way knowledge K that can be retrieved from this observable and find that K depends on the phase difference \delta that the interfering object accumulates on its way from either slit to the detector. In particular, it turns out that K(\delta) has an upper bound of 1, almost independent of the visibility V of the interference pattern generated by the interfering object on a screen, which is in marked contrast to the well-known inequality K^2 + V^2 <= 1 (cf. B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996)).Comment: 7 pages, 4 figure

ЯКІВ ДМИТРОВИЧ ГРАХОВ – ДІЯЧ КУЛЬТУРИ ТА ОСВІТИ В КАТЕРИНОСЛАВСЬКІЙ ГУБЕРНІЇ

Розглянуто життєвий шлях, освітянську, наукову та музеєзнавчу діяльність директора Катеринославської гімназії та училищ краю Якова Дмитровича Грахова в середині ХІХ ст.The article covers life, scientific and museum activities of Yakiv Dmitrovych Grakhov, a director of Katerinoslav schools in the middle of the 19th centuary

Silver Complexation by Metallacryptates

We report the first complete characterization of metallycryptates encapsulating Ag(i) cations: carboxylato ligands derived from l-proline and l-alanine chelate and bridge six Cu(ii) centres arranged in a slightly distorted octahedral fashion

Tomographic Quantum Cryptography: Equivalence of Quantum and Classical Key Distillation

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.Comment: 4 pages, 1 figur

Lattice thermal expansion and anisotropic displacements in {\alpha}-sulfur from diffraction experiments and first-principles theory

Thermal properties of solid-state materials are a fundamental topic of study with important practical implications. For example, anisotropic displacement parameters (ADPs) are routinely used in physics, chemistry, and crystallography to quantify the thermal motion of atoms in crystals. ADPs are commonly derived from diffraction experiments, but recent developments have also enabled their first-principles prediction using periodic density functional theory (DFT). Here, we combine experiments and dispersion-corrected DFT to quantify lattice thermal expansion and ADPs in crystalline {\alpha}-sulfur (S8), a prototypical elemental solid that is controlled by the interplay of covalent and van der Waals interactions. We first report on single-crystal and powder X-ray diffraction (XRD) measurements that provide new and improved reference data from 10 K up to room temperature. We then use several popular dispersion-corrected DFT methods to predict vibrational and thermal properties of {\alpha}-sulfur, including the anisotropic lattice thermal expansion. Hereafter, ADPs are derived in the commonly used harmonic approximation (in the computed zero-Kelvin structure) and also in the quasi-harmonic approximation (QHA) which takes the predicted lattice thermal expansion into account. At the PBE+D3(BJ) level, the latter leads to excellent agreement with experiments. Finally, more general implications of this study for realistic materials modeling at finite temperature are discussed

Complementarity, quantum erasure and delayed choice with modified Mach-Zehnder interferometers

Often cited dictums in Quantum Mechanics include "observation disturbance causes loss of interference" and "ignorance is interference". In this paper we propose and describe a series of experiments with modified Mach-Zehnder interferometers showing that one has to be careful when applying such dictums. We are able to show that without interacting in any way with the light quantum (or quanta) expected to behave "wave-like", interference fringes can be lost by simply gaining (or having the potential to gain) the which-path knowledge. Erasing this information may revive the interference fringes. Delayed choice can be added, arriving to an experiment in line with Wheeler's original proposal. We also show that ignorance is not always synonym with having the interference fringes. The often-invoked "collapse of the wavefunction" is found to be a non-necessary ingredient to describe our experiments.Comment: 8 pages, 3 figures; to appear in EPJ