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In this paper, we derive a general formula of the tangle for pure states of three qubits, and present three explicit local unitary (LU) polynomial invariants. Our result goes beyond the classical work of tangle, 3-tangle and von Neumann entropy of entanglement for Ac\'{\i}n et al.' Schmidt decomposition (ASD) of three qubits by connecting the tangle, 3-tangle, and von Neumann entropy for ASD with Ac\'{\i}n et al.'s LU invariants. In particular, our result reveals a general relation among tangle, 3-tangle, and von Neumann entropy, together with a relation among their averages. The relations can help us find the entangled states satisfying distinct requirements for tangle, 3-tangle, and von Neumann entropy. Moreover, we obtain all the states of three qubits of which tangles, concurrence, 3-tangle and von Neumann entropy don't vanish and these states are endurable when one of three qubits is traced out. We indicate that for the three-qubit W state, its average von Neumann entropy is maximal only within the W SLOCC class, and that under ASD the three-qubit GHZ state is the unique state of which the reduced density operator obtained by tracing any two qubits has the maximal von Neumann entropy., Comment: 14 pages, no figure

The total amount of dust grains in protoplanetary disks is one of the key properties that characterize the potential for planet formation. With (sub-)millimeter flux measurements, literature studies usually derive the dust mass using an analytic form under the assumption of optically thin emission, which may lead to substantial underestimation. In this work, we conduct a parameter study with the goal of investigating the effects of disk structure and dust properties on the underestimation through self-consistent radiative transfer models. Different dust models, scattering modes and approaches for dust settling are considered and compared. The influences of disk substructures, such as rings and crescents, on the mass derivation are investigated as well. The results indicate that the traditional analytic method can underestimate the mass by a factor of a few to hundreds, depending on the optical depth along the line of sight set mainly by the true dust mass, disk size and inclination. As an application, we perform a detailed radiative transfer modeling of the spectral energy distribution of DoAr 33, one of the observed DSHARP disks. When the DSHARP dust opacities are adopted, the most probable dust mass returned from the Bayesian analysis is roughly 7 times higher than the value given by the analytic calculation. Our study demonstrates that estimating disk dust masses from radiative transfer modeling is one solution for alleviating the problem of insufficient mass for planet formation raised in the ALMA era., Comment: 16 pages, 9 figures, accepted for publication in A&A

In [Phys. Rev. Lett. 105, 100507 (2010)], Borsten et al. derived 31 entanglement families of four qubits by using the black-hole vs. qubit correspondence, which can be reduced to nine up to permutation of the four qubits under stochastic local operations and classical communication (SLOCC). In this paper, we investigate the classification of "large" black holes by using the local unitary operator (LU) entanglement classification of three qubits. We relate the LU entanglement classes of the GHZ SLOCC class of three qubits to different classes of "large" black holes. Thus, we partition "large" black holes into seven inequivalent families. We show that between two black holes with four non-vanishing charges $q_{0}$, $p^{1}$, $p^{2}$, and $p^{3}$, if the only difference is the signs of the charges, then they are LU equivalent. Thus, the partition of black holes is independent of the signs of the charges and is only related to the ratio of the absolute charges.

Rotating wave approximation (RWA) plays a key rule in quantum optics to solve some Schr\"{o}dinger equation approximately. For example, it is well known that RWA has been used to calculate the transition probability. However, so far no one shows the validity of RWA. Recently Larson [J. Larson, Phys. Rev. Lett. 108, 033601 (2012)] gave the first example showing that the application of RWA in the Jaynes-Cummings model may lead to false conclusions. In this paper, we analytically and numerically show that the application of RWA leads to false conclusions about the transition probability for the near or exact resonance., Comment: 14 pages, 2 figures This paper has been withdrawn by the authors because Eq. (22) holds only for some case and the figures ploted from the data obtained with 15*10^{6} iterations are not precice. The figures will be ploted with 15*10^{8}iterations to solve the ode by using workstation

In this paper we derived the precise formula in a sine function form of the norm of the amplitude in the desired state, and by means of he precise formula we presented the necessary and sufficient phase condition for any quantum algorithm with arbitrary phase rotations. We also showed that the phase condition: identical rotation angles, is a sufficient but not a necessary phase condition., 16 pages. Modified some English sentences and some proofs. Removed a table. Corrected the formula for kol on page 10. No figures

This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm being optimal among the algorithms with arbitrary phase rotations was given in this paper. This first reported the non-symmetric effects of different rotating angles, and gave the first-order approximate phase condition when rotating angles are different., 13 pages, misusing tex formatting commands in title, shorted the titles, corrected typos, added the justifications to the section 2