A complete criterion for separability detection

Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of efficiently solvable semidefinite programs. We apply this method to derive arbitrarily good approximations to the optimal measure-and-prepare strategy in generic state estimation problems. Finally, we report its performance in combination with the criterion developed by Doherty et al. [1] for the calculation of the entanglement robustness of a relevant family of quantum states whose separability properties were unknown

Resolving Neutrino Mass Hierarchy and CP Degeneracy by Two Identical Detectors with Different Baselines

We explore the possibility of simultaneous determination of neutrino mass hierarchy and the CP violating phase by using two identical detectors placed at different baseline distances. We focus on a possible experimental setup using neutrino beam from J-PARC facility in Japan with beam power of 4MW and megaton (Mton)-class water Cherenkov detectors, one placed in Kamioka and the other at somewhere in Korea. We demonstrate, under reasonable assumptions of systematic uncertainties, that the two-detector complex with each fiducial volume of 0.27 Mton has potential of resolving neutrino mass hierarchy up to sin^2 2theta_{13} > 0.03 (0.055) at 2\sigma (3\sigma) CL for any values of delta and at the same time has the sensitivity to CP violation by 4 + 4 years running of nu_e and nu_e-bar appearance measurement. The significantly enhanced sensitivity is due to clean detection of modulation of neutrino energy spectrum, which is enabled by cancellation of systematic uncertainties between two identical detectors which receive the neutrino beam with the same energy spectrum in the absence of oscillations.Comment: 23 pages, 10 figures, version published in PR

What Does mu-tau Symmetry Imply about Neutrino Mixings?

The requirement of the mu-tau symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin(\theta_{13})=0 (referred to as C1)) or sin(\theta_{12})=0 (referred to as C2)), where \theta_{12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately mu-tau symmetric textures. It is argued that the tiny mu-tau symmetry breaking generally leads to cos(2\theta_{23}) \simsin(\theta_{13}) for C1) and cos(2\theta_{23}) \sim \Delta m^2_\odot/\Delta m^2_{atm}(\equiv R) for C2), which indicates that the smallness of cos(2\theta_{23}) is a good measure of the mu-tau symmetry breaking, where \Delta m^2_{atm} (\Delta m^2_\odot) stands for the square mass differences of atmospheric (solar) neutrinos. We further find that the relation R \sim sin^2(\theta_{13}) arises from contributions of O(sin^2(\theta_{13})) in the estimation of the neutrino masses (m_{1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin^2(2\theta_{12})=O(1) for C2). To satisfy R \sim sin^2(\theta_{13}) for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with | m_{1,2,3}| \sim O(\sqrt{\Delta m^2_{atm}}), and, to realize sin^2(2\theta_{12})=O(1) for C2), there should be an additional small parameter \eta whose size is comparable to that of the mu-tau symmetry breaking parameter \epsilon, giving tan(2\theta_{12}) \sim \epsilon/\eta with \eta \sim \epsilon to be compatible with the observed large mixing.Comment: 10 pages, title slightly modified, comments added in the introdction, typos corrected, references updated, version to appear in Physical Reviews

Asymmetric function theory

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.Comment: 36 pages, 8 figures, 1 table. Written for the proceedings of the Schubert calculus conference in Guangzhou, Nov. 201

Of tissue blocks and higher anatomy: A typical day in the life of a BSc (Anatomy) student

No Abstrac

Correlation between Leptonic CP Violation and mu-tau Symmetry Breaking

Considering the $\mu$-$\tau$ symmetry, we discuss a direct linkage between phases of flavor neutrino masses and leptonic CP violation by determining three eigenvectors associated with ${\rm\bf M}=M^\dagger_\nu M_\nu$ for a complex flavor neutrino mass matrix $M_\nu$ in the flavor basis. Since the Dirac CP violation is absent in the $\mu$-$\tau$ symmetric limit, leptonic CP violation is sensitive to the $\mu$-$\tau$ symmetry breaking, whose effect can be evaluated by perturbation. It is found that the Dirac phase ($\delta$) arises from the $\mu$-$\tau$ symmetry breaking part of ${\rm\bf M}_{e\mu,e\tau}$ and an additional phase ($\rho$) is associated with the $\mu$-$\tau$ symmetric part of ${\rm\bf M}_{e\mu,e\tau}$, where ${\rm\bf M}_{ij}$ stands for an $ij$ matrix element ($i,j$=$e,\mu,\tau$). The phase $\rho$ is redundant and can be removed but leaves its effect in the Dirac CP violation characterized by $\sin (\delta + \rho)$. The perturbative results suggest the exact formula of mixing parameters including that of $\delta$ and $\rho$, which turns out to be free from the effects of the redundant phases. As a result, it is generally shown that the maximal atmospheric neutrino mixing necessarily accompanies either $\sin\theta_{13}=0$ or $\cos(\delta+\rho)=0$, the latter of which indicates maximal CP violation, where $\theta_{13}$ is the $\nu_e$-$\nu_\tau$ mixing angle.Comment: 16 pages, ReVTeX, references updated, typos corredcted, published version in Physical Reviews

Neutrino Mass Textures with Maximal CP Violation

We have found three types of neutrino mass textures, which give maximal CP-violation as well as maximal atmospheric neutrino mixing. These textures are described by six real mass parameters: one specified by two complex flavor neutrino masses and two constrained ones and the others specified by three complex flavor neutrino masses. In each texture, we calculate mixing angles and masses as well as Majorana CP phases.Comment: 10 pages, RevTex, no figures, references updated, version to appear in Phys. Rev.

The power of symmetric extensions for entanglement detection

In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N -extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.Comment: see Video Abstract at http://www.quantiki.org/video_abstracts/0906273