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We put forward complementary relations of entanglement, coherence, steering inequality violation, and Bell nonlocality for arbitrary three-qubit states. We show that two families of genuinely entangled three-qubit pure states with single parameter exist, and they exhibit maximum coherence and steering inequality violation for a fixed amount of negativity, respectively. It is found that the negativity is exactly equal to the geometric mean of bipartite concurrences for the three-qubit pure states, although the negativity is always less than or equal to the latter for three-qubit mixed states. Moreover, the complementary relation between negativity and first-order coherence for tripartite entanglement states are established. Furthermore, we investigate the close relation between the negativity and the maximum steering inequality violation. In addition, the complementary relation between negativity and the maximum Bell-inequality violation for arbitrary three-qubit states is obtained. The results provide reliable evidence of fundamental connections among entanglement, coherence, steering inequality violation, and Bell nonlocality., Comment: 11 pages, 5 figures

We present an analysis of physical properties of 34 [O III] emission-line galaxies (ELGs) at z=3.254$\pm$0.029 in the Extended Chandra Deep Field South (ECDFS). These ELGs are selected from deep narrow H2S(1) and broad Ks imaging of 383 arcmin$^{2}$ obtained with CFHT/WIRCam. We construct spectral energy distributions (SEDs) from U to Ks to derive the physical properties of ELGs. These [O III] ELGs are identified as starburst galaxies with strong [O III] lines of L([O III]) ~ 10$^{42.6}$ - 10$^{44.2}$ erg s$^{-1}$, and have stellar masses of M* ~ 10$^{9.0}$-10$^{10.6}$ M$_\odot$ and star formation rates of ~ 10-210 M$_\odot$ yr$^{-1}$. Our results show that 24% of our sample galaxies are dusty with Av > 1 mag and EW(OIII)$_{rest}$ ~ 70-500 $\AA$, which are often missed in optically selected [O III] ELG samples. Their rest-frame UV and optical morphologies from HST/ACS and HST/WFC3 deep imaging reveal that these [O III] ELGs are mostly multiple-component systems (likely mergers) or compact. And 20% of them are nearly invisible in the rest-frame UV owing to heavy dust attenuation. Interestingly, we find that our samples reside in an overdensity consisting of two components: one southeast (SE) with an overdensity factor of $\delta_{gal}$ ~ 41 over a volume of 13$^{3}$ cMpc$^{3}$ and the other northwest (NW) with $\delta_{gal}$ ~ 38 over a volume of 10$^{3}$ cMpc$^{3}$. The two overdense substructures are expected to be virialized at z=0 with a total mass of ~ 1.1 x 10$^{15}$ M$_\odot$ and ~ 4.8 x 10$^{14}$ M$_\odot$, and probably merge into a Coma-like galaxy cluster., Comment: 22 pages, 11 figures, 3 tables. Accepted for publication in ApJ

In quantum resource theories (QRTs), there exists evidences of intrinsic connections among different measures of quantum resources, including entanglement, coherence, quantum steering, and so on. However, building the relations among different quantum resources is a vital yet challenging task in multipartite quantum systems. Here, we focus on a unified framework of interpreting the interconversions among different quantum resources in tripartite systems. In particular, an exact relation between the generalized geometric measure and the genuinely multipartite concurrence are derived for tripartite entanglement states. Then we obtain the tradeoff relation between the first-order coherence and the genuine tripartite entanglement by the genuinely multipartite concurrence and concurrence fill. Furthermore, the tradeoff relation between the maximum steering inequality violation and concurrence fill for an arbitrary three-qubit pure state is found. In addition, we investigate the close relation between the maximum steering inequality violation and the first-order coherence. The results show that these quantum resources are intrinsic related and can be converted to each other in the framework of QRTs, although they are still regarded to be different., Comment: 12 pages, 5 figures

We report the first spatially resolved measurements of gas-phase metallicity radial gradients in star-forming galaxies in overdense environments at $z\gtrsim2$. The spectroscopic data are acquired by the \mg\ survey, a Hubble Space Telescope (HST) cycle-28 medium program. This program is obtaining 45 orbits of WFC3/IR grism spectroscopy in the density peak regions of three massive galaxy protoclusters (BOSS 1244, BOSS 1542 and BOSS 1441) at $z=2-3$. Our sample in the BOSS 1244 field consists of 20 galaxies with stellar-mass ranging from $10^{9.0}$ to $10^{10.3}$ \Msun\ , star formation rate (SFR) from 10 to 240 \Msun\,yr$^{-1}$, and global gas-phase metallicity (\oh) from 8.2 to 8.6. At $1\sigma$ confidence level, 2/20 galaxies in our sample show positive (inverted) gradients -- the relative abundance of oxygen increasing with galactocentric radius, opposite the usual trend. Furthermore, 1/20 shows negative gradients and 17/20 are consistent with flat gradients. This high fraction of flat/inverted gradients is uncommon in simulations and previous observations conducted in blank fields at similar redshifts. To understand this, we investigate the correlations among various observed properties of our sample galaxies. We find an anticorrelation between metallicity gradient and global metallicity of our galaxies residing in extreme overdensities, and a marked deficiency of metallicity in our massive galaxies as compared to their coeval field counterparts. We conclude that the cold-mode gas accretion plays an active role in shaping the chemical evolution of galaxies in the protocluster environments, diluting their central chemical abundance, and flattening/inverting their metallicity gradients., Comment: 13 pages, 6 figures, 1 table. Accepted for publication in ApJL