Complete solution for unambiguous discrimination of three pure states with real inner products

Complete solutions are given in a closed analytic form for unambiguous discrimination of three general pure states with real mutual inner products. For this purpose, we first establish some general results on unambiguous discrimination of n linearly independent pure states. The uniqueness of solution is proved. The condition under which the problem is reduced to an (n-1)-state problem is clarified. After giving the solution for three pure states with real mutual inner products, we examine some difficulties in extending our method to the case of complex inner products. There is a class of set of three pure states with complex inner products for which we obtain an analytical solution.Comment: 13 pages, 3 figures, presentation improved, reference adde

Information theoretical properties of Tsallis entropies

A chain rule and a subadditivity for the entropy of type $\beta$, which is one of the nonadditive entropies, were derived by Z.Dar\'oczy. In this paper, we study the further relations among Tsallis type entropies which are typical nonadditive entropies. The chain rule is generalized by showing it for Tsallis relative entropy and the nonadditive entropy. We show some inequalities related to Tsallis entropies, especially the strong subadditivity for Tsallis type entropies and the subadditivity for the nonadditive entropies. The subadditivity and the strong subadditivity naturally lead to define Tsallis mutual entropy and Tsallis conditional mutual entropy, respectively, and then we show again chain rules for Tsallis mutual entropies. We give properties of entropic distances in terms of Tsallis entropies. Finally we show parametrically extended results based on information theory.Comment: The subsection on data processing inequality was deleted. Some typo's were modifie

Discrimination with error margin between two states - Case of general occurrence probabilities -

We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence probabilities. The optimal measurements are classified into three types. One of the three types of measurement is optimal depending on parameters (occurrence probabilities and error margin). We determine the three domains in the parameter space and the optimal discrimination success probability in each domain in a fully analytic form. It is also shown that when the states to be discriminated are multipartite, the optimal success probability can be attained by local operations and classical communication. For discrimination of two mixed states, an upper bound of the optimal success probability is obtained.Comment: Final version, 9 pages, references added, presentation improve

Charge-stripe order in the electronic ferroelectric LuFe2O4

The structural features of the charge ordering states in LuFe2O4 are characterized by in-situ cooling TEM observations from 300K down to 20K. Two distinctive structural modulations, a major q1= (1/3, 1/3, 2) and a weak q2=q1/10 + (0, 0, 3/2), have been well determined at the temperature of 20K. Systematic analysis demonstrates that the charges at low temperatures are well crystallized in a charge stripe phase, in which the charge density wave behaviors in a non-sinusoidal fashion resulting in elemental electric dipoles for ferroelectricity. It is also noted that the charge ordering and ferroelectric domains often change markedly with lowering temperatures and yields a rich variety of structural phenomena.Comment: 15 pages, 4 figure

Stationary quantum Markov process for the Wigner function

As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase space, each particle can be treated independently. This is an improvement on earlier methods that require the whole distribution function to determine the evolution of a constituent particle. The process has branching and vanishing points, though a finite time interval can be maintained between the branchings. The procedure to perform a simulation using the process is presented.Comment: 12 pages, no figures; replaced with version accepted for publication in J. Phys. A, title changed, an example adde

Control of nanostructures by cooling rate in spinel-type manganese oxide ZnMnGaO4

Controllability of the nanostructures in spinel-type manganese oxide ZnMnGaO4 by changing cooling rate was studied via transmission electron microscopy (with selected area electron diffraction and bright- and dark-field imaging) as well as X-ray diffraction. The Quench sample exhibited a tweed pattern, suggesting the coexistence of two phases at the nanometer scale. The nanostructural changes from a fine twin structure to a checkerboard nanostructure, followed by the emergence of a lamellar-type nanostructure, were clearly observed as the cooling rate decreased from quenching to 1 °C h−1. It was suggested that the diffusion of manganese ions accompanied by the Jahn–Teller distortion play an important role in the formation of nanostructures of this system

Epitaxial checkerboard arrangement of nanorods in ZnMnGaO4 films studied by x-ray diffraction

The intriguing nano-structural properties of a ZnMnGaO4 film epitaxially grown on MgO (001) substrate have been investigated using synchrotron radiation-based x-ray diffraction. The ZnMnGaO4 film consisted of a self-assembled checkerboard (CB) structure with perfectly aligned and regularly spaced vertical nanorods. The lattice parameters of the orthorhombic and rotated tetragonal phases of the CB structure were analyzed using H-K, H-L, and K-L cross sections of the reciprocal space maps measured around various symmetric and asymmetric reflections of the spinel structure. We demonstrate that the symmetry of atomic displacements at the phases boundaries provides the means for coherent coexistence of two domains types within the volume of the film

Retinal nerve fiber layer photography as an indicator of nerve fiber integrity in ocular hypertensive subjects

To evaluate the usefulness of retinal nerve fiber layer (RNFL) photography in the estimation of nerve fiber layer integrity in ocular hypertensive subjects; we examined 89 eyes of normal (59 eyes, 48 subjects), ocular hypertensive (26 eyes, 14 subjects), and glaucomatous (4 eyes, 2 subjects) patients. Preliminary studies included verification of the Statpac program for the Humphrey field analyzer, and establishing the method of nerve fiber layer photography sensitive enough to detect nerve fiber layer loss. The main study matched 14 ocular hypertensive subjects with 14 normal subjects. The subjects were matched by age(+/- 5 years), sex, and race. It was found that 2 of the 59 total normal eyes (3.4%) [ 2 of the 48 normal subjects (4.2%)]; 2 of the 15 matched normal eyes (13.3%) [2 of 14 matched normal subjects (14.3%)]; and 2 of 24 assessable ocular hypertensive eyes (8.3%) [2 of 13 subjects (15.4%)] showed suspected focal nerve fiber layer defects. None of our normal or ocular hypertensive subjects showed diffuse nerve fiber layer loss. We feel that retinal nerve fiber layer photography is a valuable indicator of nerve fiber layer integrity

Structural Transition of Li2RuO3 Induced by Molecular-Orbit Formation

A pseudo honeycomb system Li2RuO3 exhibits a second-order-like transition at temperature T=Tc=540 K to a low-T nonmagnetic phase with a significant lattice distortion forming Ru-Ru pairs. For this system, we have calculated the band structure, using the generalized gradient approximation (GGA) in both the high- and low- T phases, and found that the results of the calculation can naturally explain the insulating behavior observed in the low-T phase. The detailed characters of the Ru 4d t2g bands obtained by the tight-binding fit to the calculated dispersion curves show clear evidence that the structural transition is driven by the formation of the Ru-Ru molecular-orbits, as proposed in our previous experimental studies.Comment: 5 pages, 5 figures, 4 tables, submitted to J. Phys. Soc. Jp