Entanglement criteria for Dicke states

Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the vicinity of these states. We use the approach of PPT mixtures to derive the conditions analytically. For nearly all cases, our criteria are stronger than all conditions previously known.Comment: 18 pages, 4 figures; updated to match published versio

RXJ0848.6+4453: The Evolution of Galaxy Sizes and Stellar Populations in a z=1.27 Cluster

RXJ0848.6+4453 (Lynx W) at redshift 1.27 is part of the Lynx Supercluster of galaxies. Our analysis of stellar populations and star formation history in the cluster covers 24 members and is based on deep optical spectroscopy from Gemini North and imaging data from HST. Focusing on the 13 bulge-dominated galaxies for which we can determine central velocity dispersions, we find that these show a smaller evolution of sizes and velocity dispersions than reported for field galaxies and galaxies in poorer clusters. The galaxies in RXJ0848.6+4453 populate the Fundamental Plane similar to that found for lower redshift clusters with a zero point offset corresponding to an epoch of last star formation at z_form= 1.95+-0.2. The spectra of the galaxies in RXJ0848.6+4453 are dominated by young stellar populations at all galaxy masses and in many cases show emission indicating low level on-going star formation. The average age of the young stellar populations (estimated from H-zeta) is consistent with a major star formation episode 1-2 Gyr prior, which in turn agrees with z_form=1.95. Galaxies dominated by young stellar populations are distributed throughout the cluster. We speculate that low level star formation has not yet been fully quenched in the center of this cluster may be because the cluster is significantly poorer than other clusters previously studied at similar redshifts, which appear to have very little on-going star formation in their centers.Comment: Accepted for publication in Astronomical Journal. High-resolution figures available from the first author by reques

RXJ0152.7-1357: Stellar populations in an X-ray luminous galaxy cluster at z=0.83

We present a study of the stellar populations of galaxies in the cluster RXJ0152.7-1357 at a redshift of 0.83. The study is based on new high S/N spectroscopy of 29 cluster members covering the wavelength range 5000-10000A as well as r'i'z' photometry of the cluster. The scaling relations between velocity dispersions, luminosities and Balmer line strengths appear to be in agreement with pure passive evolution of the stellar populations with a formation redshift z=4. However, the strengths of the D4000 indices and the metal indices do not support this interpretation. Compared to z=0, the metal indices (C4668, Fe4383, CN3883, G4300 and CN2) show that at least half of the non-emission line galaxies in RXJ0152.7-1357 have [alpha/Fe] of 0.2 dex higher, and about half of the galaxies have significantly lower metal content. The differences in stellar populations of the galaxies are associated with the location of the galaxies relative to the X-ray emission. The galaxies with weak C4668 and G4300, as well as galaxies with weak [OII] emission, are located in areas of low X-ray luminosity. It is possible that these galaxies are experiencing the effect of the cluster merger taking place in RXJ0152.7-1357 as (short) episodes of star formation, while the galaxies in the cores of the X-ray sub-clumps are unaffected by the merger. The spectroscopy of the RXJ0152.7-1357 galaxies shows for the first time galaxies in a rich cluster at intermediate redshift that cannot evolve passively into the present day galaxy population in rich clusters. Additional physical processes may be at work and we speculate that merging with infalling (disk) galaxies in which stars have formed over an extended period might produce the required reduction in [alpha/Fe]. (abridged)Comment: Accepted for publication in Astronomical Journal, 39 pages, uses emulateapj.cls, 18 figures. High resolution color figures available by e-mail request to the first autho

Nonlinear quantum error correction

We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords. However, this can be more general than required for a given quantum protocol which may only traverse a subclass of states within the Hilbert space. Here we propose the concept of nonlinear QEC (NLQEC), where the encoded states are not necessarily a linear combination of codewords. We introduce a sufficiency criterion for NLQEC with respect to the subclass of states. The new criterion gives a more relaxed condition for the formation of a QEC code, such that under the assumption that the states are within the subclass of states, the errors are correctable. This allows us, for instance, to effectively circumvent the no-go theorems regarding optical QEC for Gaussian states and channels, for which we present explicit examples