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Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the $l_1$-norm measure of coherence for convex combination of arbitrary $n$ pure states of a quantum state $\rho$. Furthermore, we present triangle-like inequality for the convex-roof extended negativity for any states of rank 2, which gives a positive answer to a conjecture raised in [Phys. Rev. A 96, 062308 (2017)]. Detailed examples are given to illustrate the relations characterized by the triangle-like inequalities.

Despite many decades of study, the kinematics of the broad-line region of 3C~273 are still poorly understood. We report a new, high signal-to-noise, reverberation mapping campaign carried out from November 2008 to March 2018 that allows the determination of time lags between emission lines and the variable continuum with high precision. The time lag of variations in H$\beta$ relative to those of the 5100 Angstrom continuum is $146.8_{-12.1}^{+8.3}$ days in the rest frame, which agrees very well with the Paschen-$\alpha$ region measured by the GRAVITY at The Very Large Telescope Interferometer. The time lag of the H$\gamma$ emission line is found to be nearly the same as for H$\beta$. The lag of the Fe II emission is $322.0_{-57.9}^{+55.5}$ days, longer by a factor of $\sim$2 than that of the Balmer lines. The velocity-resolved lag measurements of the H$\beta$ line show a complex structure which can be possibly explained by a rotation-dominated disk with some inflowing radial velocity in the H$\beta$-emitting region. Taking the virial factor of $f_{\rm BLR} = 1.3$, we derive a BH mass of $M_{\bullet} = 4.1_{-0.4}^{+0.3} \times 10^8 M_{\odot}$ and an accretion rate of $9.3\,L_{\rm Edd}\,c^{-2}$ from the H$\beta$ line. The decomposition of its $HST$ images yields a host stellar mass of $M_* = 10^{11.3 \pm 0.7} M_\odot$, and a ratio of $M_{\bullet}/M_*\approx 2.0\times 10^{-3}$ in agreement with the Magorrian relation. In the near future, it is expected to compare the geometrically-thick BLR discovered by the GRAVITY in 3C 273 with its spatially-resolved torus in order to understand the potential connection between the BLR and the torus., Comment: 17 pages, 12 figures, 6 tables, accepted for publication in The Astrophysical Journal

NGC 5548 has been well spectroscopically monitored for reverberation mapping of the central kinematics by 19 campaigns. Using the maximum entropy method in this Letter, we build up a high-quality velocity-delay map of the H$\beta$ emission line in the light curves of the continuum and the line variations observed between 2015-2016. The map shows the response strength and lags of the velocity fields of the H$\beta$ emitting regions. The velocity-delay structure of the map is generally symmetric, with strong red and blue wings at time lag $\tau \leq 15$ days, a narrower velocity distribution at $\tau \geq 15$ days, and a deficit of response in the core. This is suggestive of a disk geometry of the broad-line region (BLR). The relatively weaker H$\beta$ response at the longer lags in the red side indicates anisotropic emission from the outer part of the BLR. We also recover the velocity-delay maps of NGC 5548 from the historical data of 13 years to investigate the long-term variability of its BLR. In general, the BLR of NGC 5548 was switching between the inflow and virialized phases in the past years. The resultant maps of seven years reveal inflow signatures and show decreasing lags, indicating that the changes in the BLR size are related to the infalling BLR gas. The other four maps show potential disk signatures which are similar to our map., Comment: 7 pages, 5 figures, accepted for publication in The Astrophysical Journal Letters

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy relations satisfied by the concurrence of assistance and the negativity of assistance for multiqubit generalized $W$-class states. Analytical monogamy inequalities are presented for both concurrence of assistance and negativity of assistance, which are shown to be tighter than the existing ones. Detailed examples have been presented., Comment: 12 pages, 2 figures

Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated. Moreover, we present Hellinger distance-based measure of non-classical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, and but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit trade-off relation satisfied by the quantum coherence and this non-classical correlation.

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence C, the entanglement of formation E, negativity Nc and Tsallis-q entanglement Tq. Monogamy relations for the $\alpha$th power of entanglement have been derived, which are tighter than the existing entanglement monogamy relations for some classes of quantum states. Detailed examples are presented.

As one of the series of papers reporting on a large reverberation mapping campaign of super-Eddington accreting massive black holes (SEAMBHs) in active galactic nuclei (AGNs), we present the results of 10 SEAMBHs monitored spectroscopically during 2015-2017. Six of them are observed for the first time, and have generally higher 5100 \AA\ luminosities than the SEAMBHs monitored in our campaign from 2012 to 2015; the remaining four are repeat observations to check if their previous lags change. Similar to the previous SEAMBHs, the H$\beta$ time lags of the newly observed objects are shorter than the values predicted by the canonical $R_{\mathrm{H\beta}}$-$L_{5100}$ relation of sub-Eddington AGNs, by factors of $\sim2-6$, depending on the accretion rate. The four previously observed objects have lags consistent with previous measurements. We provide linear regressions for the $R_{\mathrm{H\beta}}$-$L_{5100}$ relation, solely for the SEAMBH sample and for low-accretion AGNs. We find that the relative strength of Fe II and the profile of the H$\beta$ emission line can be used as proxies of accretion rate, showing that the shortening of H$\beta$ lags depends on accretion rates. The recent SDSS-RM discovery of shortened H$\beta$ lags in AGNs with low accretion rates provides compelling evidence for retrograde accretion onto the black hole. These evidences show that the canonical $R_{\mathrm{H\beta}}$-$L_{5100}$ relation holds only in AGNs with moderate accretion rates. At low accretion rates, it should be revised to include the effects of black hole spin, whereas the accretion rate itself becomes a key factor in the regime of high accretion rates., Comment: 22 pages, 8 figures, 10 tables, accepted for publication in The Astrophysical Journal

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations for multiqubit generalized W-class states. We present new analytical monogamy inequalities for the concurrence of assistance, which are shown to be tighter than the existing ones. Furthermore, analytical monogamy inequalities are obtained for the negativity of assistance., Comment: 14 pages, 2 figures