A study of separability criteria for mixed three-qubit states

We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne and Seevinck dealing with matrix elements are the strongest ones for different separability classes of this 2 parameter state. As a new result we determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl

The attractor mechanism as a distillation procedure

In a recent paper it has been shown that for double extremal static spherically symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of GHZ-type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a GHZ state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macroscopic black hole entropy. A systematic study of such attractor states shows that their properties reflect the structure of the fake superpotential. We also demonstrate that when starting with the very special values for the moduli corresponding to flat directions the uniform structure at the horizon deteriorates due to errors generalizing the usual bit flips acting on the qubits of the attractor states.Comment: 38 pages LaTe

The Evolution of the Global Star Formation History as Measured from the Hubble Deep Field

The Hubble Deep Field (HDF) is the deepest set of multicolor optical photometric observations ever undertaken, and offers a valuable data set with which to study galaxy evolution. Combining the optical WFPC2 data with ground-based near-infrared photometry, we derive photometrically estimated redshifts for HDF galaxies with J<23.5. We demonstrate that incorporating the near-infrared data reduces the uncertainty in the estimated redshifts by approximately 40% and is required to remove systematic uncertainties within the redshift range 1<z<2. Utilizing these photometric redshifts, we determine the evolution of the comoving ultraviolet (2800 A) luminosity density (presumed to be proportional to the global star formation rate) from a redshift of z=0.5 to z=2. We find that the global star formation rate increases rapidly with redshift, rising by a factor of 12 from a redshift of zero to a peak at z~1.5. For redshifts beyond 1.5, it decreases monotonically. Our measures of the star formation rate are consistent with those found by Lilly et al. (1996) from the CFRS at z 2, and bridge the redshift gap between those two samples. The overall star formation or metal enrichment rate history is consistent with the predictions of Pei and Fall (1995) based on the evolving HI content of Lyman-alpha QSO absorption line systems.Comment: Latex format, 10 pages, 3 postscript figures. Accepted for publication in Ap J Letter