Cosmic reionization of hydrogen and helium: contribution from both mini-quasars and stars

Observations on the high-redshift galaxies at $z>6$ imply that their ionizing emissivity is unable to fully reionize the Universe at $z\sim 6$. Either a high escape fraction of ionizing photons from these galaxies or a large population of faint galaxies below the detection limit are required. However, these requirements are somewhat in tension with present observations. In this work, we explored the combined contribution of mini-quasars and stars to the reionization of cosmic hydrogen and helium. Our model is roughly consistent with: (1) the low escape fractions of ionizing photons from the observed galaxies, (2) the optical depth of Cosmic Microwave Background (CMB) measured by the WMAP-7, and (3) the redshift of the end of hydrogen and helium reionization at $z\approx 6$ and $z\approx 3$, respectively. Neither an extremely high escape fraction nor a large population of fainter galaxies is required in this scenario. In our most optimistic model, more than $\sim20\%$ of the cosmic helium is reionized by $z\sim6$, and the ionized fraction of cosmic helium rapidly climbs to more than $50\%$ by $z\sim5$. These results may imply that better measurements of helium reionization, especially at high redshifts, could be helpful in constraining the growth of intermediate-mass black holes (IMBHs) in the early Universe, which would shed some light on the puzzles concerning the formation of supermassive black holes (SMBHs).Comment: 11 pages, 7 figures, accepted for publication in MNRA

Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

Taking into account the density matrices with non-full ranks, we show that the fidelity susceptibility is determined by the support of the density matrix. Combining with the corresponding expression of the quantum Fisher information, we rigorously prove that the fidelity susceptibility is proportional to the quantum Fisher information. As this proof can be naturally extended to the full rank case, this proportional relation is generally established for density matrices with arbitrary ranks. Furthermore, we give an analytical expression of the quantum Fisher information matrix, and show that the quantum Fisher information matrix can also be represented in the density matrix's support.Comment: 10 pages, no figur

Quantum Separability Criteria for Arbitrary Dimensional Multipartite States

We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our criteria are more powerful than the positive partial transposition criterion, the realignment criterion and the criteria based on the correlation matrices.Comment: 11 page

Photoelectron angular distribution from the high-order above-threshold ionization process in IR+XUV two-color laser fields

High-order above-threshold ionization (HATI) spectrum in IR+XUV two-color laser fields has been investigated. We found that the quantum features corresponding to the absorption of the XUV photon is well illustrated by a peculiar dip structure in the second plateau of the HATI spectrum. By the channel analysis, we show that the angular distribution of the spectrum is attributed to the coherent summation over contributions of different channels, and the dip structure in the spectrum is directly related to the absorption of one XUV photon of the ionized electron during the laser-assisted collision (LAC) with its parent ion in the two-color laser fields. Moreover, by employing the saddle-point approximation, we obtain the classical energy orbit equation, and find that the dip structure comes from the fact that the LAC is limited at a certain direction by the momentum conservation law as the electron absorbs one XUV photon during the collision, where the probability of the HATI gets its minimum value. Finally, we find that the interference pattern in the whole spectrum is attributed to the interference of different orbits at collision moments $t_0$ and $2\pi/\omega_1-t_0$ in the LAC process

Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic Optimization

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In this paper, we propose a novel and fast robust matrix completion method based on maximum correntropy criterion (MCC). The correntropy based error measure is utilized instead of using $l_2$-based error norm to improve the robustness to noises. Using the half-quadratic optimization technique, the correntropy based optimization can be transformed to a weighted matrix factorization problem. Then, two efficient algorithms are derived, including alternating minimization based algorithm and alternating gradient descend based algorithm. The proposed algorithms do not need to calculate singular value decomposition (SVD) at each iteration. Further, the adaptive kernel selection strategy is proposed to accelerate the convergence speed as well as improve the performance. Comparison with existing robust matrix completion algorithms is provided by simulations, showing that the new methods can achieve better performance than existing state-of-the-art algorithms

Detection and measure of genuine tripartite entanglement with partial transposition and realignment of density matrices

It is challenging task to detect and measure genuine multipartite entanglement. We investigate the problem by considering the average based positive partial transposition(PPT) criterion and the realignment criterion. Sufficient conditions for detecting genuine tripartite entanglement are presented. We also derive lower bounds for the genuine tripartite entanglement concurrence with respect to the conditions. While the PPT criterion and the realignment criterion are powerful for detecting bipartite entanglement and for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and measure the genuine tripartite entanglement.Comment: 10 pages, 2 figure

A complex network analysis of hypertension-related genes

In this paper, a network of hypertension-related genes is constructed by analyzing the correlations of gene expression data among the Dahl salt-sensitive rat and two consomic rat strains. The numerical calculations show that this sparse and assortative network has small-world and scale-free properties. Further, 16 key hub genes (Col4a1, Lcn2, Cdk4, etc.) are determined by introducing an integrated centrality and have been confirmed by biological/medical research to play important roles in hypertension.Comment: 13 pages, 6 figures, 3 tables; a revised version of an article published in Physica A: Statistical Mechanics and its Application

Measure and detection of genuine multipartite entanglement for tripartite systems

It is a computationally hard task to certify genuine multipartite entanglement (GME). We investigate the relation between the norms of the correlation vectors and the detection of GME for tripartite quantum systems. A sufficient condition for GME and an effective lower bound for the GME concurrence are derived. Several examples are considered to show the effectiveness of the criterion and the lower bound of GME concurrence.Comment: 6 pages, 4 figure

Improving cosmological parameter estimation with the future gravitational-wave standard siren observation from the Einstein Telescope

Detection of gravitational waves produced by merger of binary compact objects could provide an independent way for measuring the luminosity distance to the gravitational-wave burst source, indicating that gravitational-wave observation, combined with observation of electromagnetic counterparts, can provide "standard sirens" for investigating the expansion history of the universe in cosmology. In this work, we wish to investigate how the future gravitational-wave standard siren observations would break the parameter degeneracies existing in the conventional optical observations and how they help improve the parameter estimation in cosmology. We take the third-generation ground-based gravitational-wave detector, the Einstein Telescope, as an example to make an analysis. By simulating 1000 events data in the redshift range between 0 and 5 based on the ten-year observation of the Einstein Telescope, we find that the gravitational-wave data could largely break the degeneracy between the matter density and the Hubble constant, thus significantly improving the cosmological constraints. We further show that the constraint on the equation-of-state parameter of dark energy could also be significantly improved by including the gravitational-wave data in the cosmological fit.Comment: 7 pages, 4 figures; accepted for publication in Physical Review

Non-commutativity and Local Indistinguishability of Quantum States

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is given. The non-commutativity of ensembles can be also used to characterize the quantumness for classical-quantum or quantum-classical correlated states.Comment: 12 page