On the Key-Uncertainty of Quantum Ciphers and the Computational Security of One-way Quantum Transmission

We consider the scenario where Alice wants to send a secret (classical) $n$-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to obtain perfect secrecy with key length smaller then $n$. We study the question of whether there might still be fundamental differences between the case where quantum as opposed to classical communication is used. In this direction, we show that there exist ciphers with perfect security producing quantum ciphertext where, even if an adversary knows the plaintext and applies an optimal measurement on the ciphertext, his Shannon uncertainty about the key used is almost maximal. This is in contrast to the classical case where the adversary always learns $n$ bits of information on the key in a known plaintext attack. We also show that there is a limit to how different the classical and quantum cases can be: the most probable key, given matching plain- and ciphertexts, has the same probability in both the quantum and the classical cases. We suggest an application of our results in the case where only a short secret key is available and the message is much longer.Comment: 19 pages, 2 figures. This is a revised version of an earlier version that appeared in the proc. of Eucrocrypt'04:LNCS3027, 200

On free energies of the Ising model on the Cayley tree

We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly periodic Gibbs states. The later are defined through a partition of the tree that induces a 4-edge-coloring. We compute the density of each color.Comment: 18 pages, 4 figure

The Pulse Scale Conjecture and the Case of BATSE Trigger 2193

The pulses that compose gamma-ray bursts (GRBs) are hypothesized to have the same shape at all energies, differing only by scale factors in time and amplitude. This "Pulse Scale Conjecture" is confirmed here between energy channels of the dominant pulse in GRB 930214c (BATSE trigger 2193), the single most fluent single-pulsed GRB that occurred before May 1998. Furthermore, pulses are hypothesized to start at the same time independent of energy. This "Pulse Start Conjecture" is also confirmed in GRB 930214c. Analysis of GRB 930214c also shows that, in general, higher energy channels show shorter temporal scale factors. Over the energy range 100 KeV - 1 MeV, it is found that the temporal scale factors between a pulse measured at different energies are related to that energy by a power law, possibly indicating a simple relativistic mechanism is at work. To test robustness, the Pulse Start and Pulse Scale Conjectures were also tested on the four next most fluent single-pulse GRBs. Three of the four clearly passed, with a second smaller pulse possibly confounding the discrepant test. Models where the pulse rise and decay are created by different phenomena do not typically predict pulses that satisfy both the Pulse Start Conjecture and the Pulse Scale Conjecture, unless both processes are seen to undergo common time dilation.Comment: 19 pages, 9 figures, analysis revised and extended, accepted to Ap

Feynman-Hellmann theorem for resonances and the quest for QCD exotica

The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible.Comment: 26 pages, 2 figure

Different scenarios of dynamic coupling in glassy colloidal mixtures

Colloidal mixtures represent a versatile model system to study transport in complex environments. They allow for a systematic variation of the control parameters, namely size ratio, total volume fraction and composition. We study the effects of these parameters on the dynamics of dense suspensions using molecular dynamics simulations and differential dynamic microscopy experiments. We investigate the motion of the small particles through the matrix of large particles as well as the motion of the large particles. A particular focus is on the coupling of the collective dynamics of the small and large particles and on the different mechanisms leading to this coupling. For large size ratios, about 1:5, and an increasing fraction of small particles, the dynamics of the two species become increasingly coupled and reflect the structure of the large particles. This is attributed to the dominant effect of the large particles on the motion of the small particles which is mediated by the increasing crowding of the small particles. Furthermore, for moderate size ratios, about 1:3, and sufficiently high fractions of small particles, mixed cages are formed and hence the dynamics are also strongly coupled. Again, the coupling becomes weaker as the fraction of small particles is decreased. In this case, however, the collective intermediate scattering function of the small particles shows a logarithmic decay corresponding to a broad range of relaxation times

Molecular Gas and Star Formation in the Cartwheel

Atacama Large Millimeter/submillimeter Array (ALMA) 12CO(J=1-0) observations are used to study the cold molecular ISM of the Cartwheel ring galaxy and its relation to HI and massive star formation (SF). CO moment maps find $(2.69\pm0.05)\times10^{9}$ M$_{\odot}$ of H$_2$ associated with the inner ring (72%) and nucleus (28%) for a Galactic I(CO)-to-N(H2) conversion factor ($\alpha_{\rm CO}$). The spokes and disk are not detected. Analysis of the inner ring's CO kinematics show it to be expanding ($V_{\rm exp}=68.9\pm4.9$ km s$^{-1}$) implying an $\approx70$ Myr age. Stack averaging reveals CO emission in the starburst outer ring for the first time, but only where HI surface density ($\Sigma_{\rm HI}$) is high, representing $M_{\rm H_2}=(7.5\pm0.8)\times10^{8}$ M$_{\odot}$ for a metallicity appropriate $\alpha_{\rm CO}$, giving small $\Sigma_{\rm H_2}$ ($3.7$ M$_{\odot}$ pc$^{-2}$), molecular fraction ($f_{\rm mol}=0.10$), and H$_2$ depletion timescales ($\tau_{\rm mol} \approx50-600$ Myr). Elsewhere in the outer ring $\Sigma_{\rm H_2}\lesssim 2$ M$_{\odot}$ pc$^{-2}$, $f_{\rm mol}\lesssim 0.1$ and $\tau_{\rm mol}\lesssim 140-540$ Myr (all $3\sigma$). The inner ring and nucleus are H$_2$-dominated and are consistent with local spiral SF laws. $\Sigma_{\rm SFR}$ in the outer ring appears independent of $\Sigma_{\rm H_2}$, $\Sigma_{\rm HI}$ or $\Sigma_{\rm HI+H_2}$. The ISM's long confinement in the robustly star forming rings of the Cartwheel and AM0644-741 may result in either a large diffuse H$_2$ component or an abundance of CO-faint low column density molecular clouds. The H$_2$ content of evolved starburst rings may therefore be substantially larger. Due to its lower $\Sigma_{\rm SFR}$ and age the Cartwheel's inner ring has yet to reach this state. Alternately, the outer ring may trigger efficient SF in an HI-dominated ISM.Comment: 10-pages text; 5-figure