Searching for Stars in Compact High-Velocity Clouds. II

We address the hypothesis that High Velocity Clouds correspond to the "missing" dwarf galaxies of the Local Group predicted by cosmological simulations. To this end, we present optical and near-infrared photometry of five additional High Velocity Clouds, one of which produces Lyman series absorption on the sight line towards the Quasar Ton S210, with sufficient resolution and sensitivity to enable the detection of an associated stellar content. We do not detect significant stellar populations intrinsic to any of the five clouds. In combination with the results from our paper I, which had yielded non detections of stellar content in another five cases, we find that there is a 50% chance of getting a null result in ten trials if fewer than 7% of all High Velocity Clouds contain stars. We conclude that the population of High Velocity Clouds is an unlikely repository for the "missing" dwarfs of the Local Group.Comment: 6 pages, 3 figures. submitted to MNRA

Searching for Stars in Compact High-Velocity Clouds. I First Results from VLT and 2MASS

We investigate the hypothesis that compact high-velocity clouds (CHVC) are the "missing" dwarf galaxies of the Local Group, by searching them for populations of resolved stars. To this end we conducted two distinct tests based on optical and near-infrared single-star photometry. The optical and the near-infrared experiments complement one another; the optical data help us to rule out distant populations but they are restricted to the central regions of the gas distributions, whereas the near-infrared photometry allows us to set limits on nearby populations spread over the typical cloud size. First, we discuss deep optical single-star photometry of five CHVCs in the V and I filters, obtained with the FORS instrument at the Very Large Telecope (VLT). We find that their optical colour-magnitude diagrams are indistinguishable from that of a population of Galactic stars, and attribute all of the resolved stars to Galactic foreground. We present simulations which address the question of how much of a "normal" dwarf-galaxy type population we might hide in the data. A Kolmogorov-Smirnov test allows us to set very stringent limits on the absence of a resolved stellar population in CHVCs. Second, we also culled near infrared single-star photometry in the J, H, and K_S bands for four of the CHVCs from the Two Micron All Sky Survey (2MASS). The infrared data do not reveal any stellar contents in the CHVCs which resembles that of nearby dwarf galaxies either, and are explained with Galactic foreground as well. We interpret our null detections to indicate that the five CHVCs investigated by us do not host an associated stellar content which is similar to that of the known dwarf galaxies of the Local Group. These CHVCs are very likely pure hydrogen clouds in which no star formation has taken place over cosmic time.Comment: 13 pages, 10 figures, accepted for publication by MNRA

Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

Motivated by applications in quantum information and quantum control, a new type of $C$"-numerical range, the relative $C$"-numerical range denoted $W_K(C,A)$, is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical $C$"-numerical range by any of its compact and connected subgroups $K \subset U(N)$. The geometric properties of the relative $C$"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. $W_K(C,A)$ is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical $C$"-numerical range extends to $W_K(C,A)$, as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup $SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2)$, i.e. the $n$-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for $W_{K}(C,A)$ being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for $SU(2) \otimes SU(2)$.Comment: accompanying paper to math-ph/070103

Optimal Control for Generating Quantum Gates in Open Dissipative Systems

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control using relaxation parameters against time-optimal control is explored and exemplified in numerical and in algebraic terms: it is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalising decoherence-free subspaces to more realistic scenarios, openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit it requires control fields orders of magnitude lower than the bang-bang decouplings in the latter.Comment: largely expanded version, superseedes v1: 10 pages, 5 figure

The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement

This paper considers the control landscape of quantum transitions in multi-qubit systems driven by unitary transformations with single-qubit interaction terms. The two-qubit case is fully analyzed to reveal the features of the landscape including the nature of the absolute maximum and minimum, the saddle points and the absence of traps. The results permit calculating the Schmidt state starting from an arbitrary two-qubit state following the local gradient flow. The analysis of multi-qubit systems is more challenging, but the generalized Schmidt states may also be located by following the local gradient flow. Finally, we show the relation between the generalized Schmidt states and the entanglement measure based on the Bures distance