Phase estimation with photon number constraint

Many researches proposed the use of the noon state as the input state for phase estimation, which is one topic of quantum metrology. This is because the input noon state provides the maximum Fisher information at the specific point. However, the Fisher information does not necessarily give the attainable bound for estimation error. In this paper, we adopt the local asymptotic mini-max criterion as well as the mini-max criterion, and show that the maximum Fisher information does not give the attainable bound for estimation error under these criteria in the phase estimation. We also propose the optimal input state under the constraints for photon number of the input state instead of the noon state.Comment: Several typos are fixed. New section "ANALYSIS ON NOON STATE" is adde

Parabolic isometries of CAT(0) spaces and CAT(0) dimensions

We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist finitely presented groups of geometric dimension 2 which do not act properly on any proper CAT(0) spaces of dimension 2 by isometries, although such actions exist on CAT(0) spaces of dimension 3. Another example is the fundamental group, G, of a complete, non-compact, complex hyperbolic manifold M with finite volume, of complex-dimension n > 1. The group G is acting on the universal cover of M, which is isometric to H^n_C. It is a CAT(-1) space of dimension 2n. The geometric dimension of G is 2n-1. We show that G does not act on any proper CAT(0) space of dimension 2n-1 properly by isometries. We also discuss the fundamental groups of a torus bundle over a circle, and solvable Baumslag-Solitar groups.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-38.abs.htm

Capture of Electroweak Multiplet Dark Matter in Neutron Stars

If dark matter has a sizable scattering cross section with nucleons, it can efficiently be captured by a neutron star. Its energy is then transferred to the neutron star as heat through the scattering and annihilation inside the star. This heating effect may be detectable via dedicated temperature observations of nearby old pulsars, providing an alternative method for dark matter searches. In this paper, we show that for electroweak multiplet dark matter this search strategy can probe the parameter region which is out of reach of future dark matter direct detection experiments. To see this systematically, we classify such dark matter candidates in terms of their electroweak charges and investigate the effect of ultraviolet physics by means of higher-dimensional effective operators. We then show that if the effect of ultraviolet physics is sizable, the dark matter-nucleon elastic scattering cross section becomes sufficiently large, whilst if it is suppressed, then the mass splittings among the components of the DM multiplet get small enough so that the inelastic scattering processes are operative. In any case, the electroweak multiplet dark matter particles are efficiently captured in neutron stars, making the search strategy with the temperature observation of old neutron stars promising.Comment: 33 pages, 7 figures, 1 tabl

Vortex Creep Heating vs. Dark Matter Heating in Neutron Stars

Dark matter particles captured in neutron stars deposit their energy as heat. This DM heating effect can be observed only if it dominates over other internal heating effects in NSs. In this work, as an example of such an internal heating source, we consider the frictional heating caused by the creep motion of neutron superfluid vortex lines in the NS crust. The luminosity of this heating effect is controlled by the strength of the interaction between the vortex lines and nuclei in the crust, which can be estimated from the many-body calculation of a high-density nuclear system as well as through the temperature observation of old NSs. We show that both the temperature observation and theoretical calculation suggest that the vortex creep heating dominates over the DM heating. The vortex-nuclei interaction must be smaller than the estimated values by several orders of magnitude to overturn this.Comment: 8 pages, 2 figure

Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation

In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the minimum mean square error decreases with the order O(1/n).Comment: In this revision, some unlcear parts are clarifie

Perturbation Analysis of Superconductivity in the Trellis-Lattice Hubbard Model

We investigate pairing symmetry and transition temperature in the trellis-lattice Hubbard model. We solve the \'Eliashberg equation using the third-order perturbation theory with respect to the on-site repulsion $U$. We find that a spin-singlet state is very stable in a wide range of parameters. On the other hand, when the electron number density is shifted from the half-filled state and the band gap between two bands is small, a spin-triplet superconductivity is expected. Finally, we discuss a possibility of unconventional superconductivity and pairing symmetry in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$.Comment: 7pages, 10 figures. To be published in J. Phys. Soc. Jp

Otimizaçâo das condições de preparação de eletrodos à base de carbono cerâmico utilizando-se planejamento fatorial

Different parameters of carbon ceramic electrodes (CCE) preparation, such as type of precursor, carbon material, catalyst amount, among others, significantly influence the morphological properties and consequently their electrochemical responses. This paper describes a 2³ factorial design (2 factors and 3 levels with central point replicates), which the factors analyzed were catalyst amount (HCl 12 mol L-1), graphite/precursor ratio, and precursor type (TEOS - tetraethoxysilane and MTMOS - methyltrimetoxysilane). The design resulted in a significant third order interaction for peak current values (Ipa) and a second order interaction for potential difference (ΔE), between thefactors studied, which could not be observed when using an univariated study

Charge-Density-Wave Formation in the Doped Two-Leg Extended Hubbard Ladder

We investigate electronic properties of the doped two-leg Hubbard ladder with both the onsite and the nearest-neighbor Coulomb repulsions, by using the the weak-coupling renormalization-group method. It is shown that, for strong nearest-neighbor repulsions, the charge-density-wave state coexisting with the p-density-wave state becomes dominant fluctuation where spins form intrachain singlets. By increasing doping rate, we have also shown that the effects of the nearest-neighbor repulsions are reduced and the system exhibits a quantum phase transition into the d-wave-like (or rung-singlet) superconducting state. We derive the effective fermion theory which describes the critical properties of the transition point with the gapless excitation of magnon. The phase diagram of the two-leg ladder compound, Sr_{14-x}Ca_xCu_{24}O_{41}, is discussed.Comment: 4 pages, 2 figure

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat