Unital quantum operators on the Bloch ball and Bloch region

For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that govern when a ``diagonal'' superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.Comment: Revised and corrected, to appear in Physical Review

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure

Multiplicativity of completely bounded p-norms implies a new additivity result

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous version deleted in view of the results in quant-ph/0601071 Other changes mino

Comments on Hastings' Additivity Counterexamples

Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the details of the proof, we also present bounds for the minimal dimensions needed to obtain a counterexample.Comment: 38 page

Flavour Universal Dynamical Electroweak Symmetry Breaking

The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry group. As an example of the higher scale dynamics a fully dynamical model of the quark sector with a GIM mechanism is presented, based on an earlier top condensation model of King using broken family gauge symmetry interactions (that model was itself based on a technicolour model of Georgi). The crucial extra ingredient is a reinterpretation of the condensates that form when several gauge groups become strong close to the same scale. A related technicolour model of Randall which naturally includes the leptons too may also be adapted to this scenario. We discuss the low energy constraints on the massive gauge bosons and scalars of these models as well as their phenomenology at the TeV scale.Comment: 22 pages, 3 fig

Clinical, angiographic and procedural correlates of quantitative coronary dimensions after directional coronary atherectomy

AbstractTo define the clinical, angiographic and procedural correlates of quantitative coronary dimensions after directional coronary atherectomy, 400 lesions in 378 patients were analyzed with use of qualitative morphologic and quantitative angiographic methods. Successful atherectomy, defined by a <75% residual area stenosis, tissue retrieval and the absence of in-hospital ischemic complications, was performed in 351 lesions (87.7%). After atherectomy, minimal cross-sectional area increased from 1.2 ± 1.1 to 6.6 ± 4.4 mm2(p < 0.001) and percent area stenosis was reduced from 87 ± 10% to 31 ± 42% (p < 0.001).By univariate analysis, device size (p < 0.001) and left circumflex artery lesion location (p = 0.004) were associated with a larger final minimal cross-sectional area. Conversely, restenotic lesion (p = 0.002), lesion length ≥ 10 mm (p = 0.018) and lesion calcification (p = 0.035) were quantitatively associated with a smaller final minimum cross-sectional area. With use of stepwise multivariate analysis to control for the reference area, atherectomy device size (p = 0.003) and left circumflex lesion location (p = 0.007) were independently associated with a larger final minimal cross-sectional area, whereas restenotic lesion (p = 0.010), diffuse proximal disease (p = 0.033), lesion length ≥ 10 mm (p = 0.026) and lesion calcification (p = 0.081) were significantly correlated with a smaller final minimal cross-sectional area. The number of specimens excised, the number of atherectomy passes and atherectomy balloon inflation pressure did not correlate with the final minimal cross-sectional area.Thus, directional atherectomy results in marked improvement of coronary lumen dimensions, at least in part correlated with the presence of certain clinical, angiographic and procedural factors at the time of atherectomy

Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p >1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors. Since p=1 corresponds to the von Neumann entropy, these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true, it cannot be proved as a consequence of any channel-independent guarantee of maximal p-norm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.Comment: Merger of arXiv:0707.0402 and arXiv:0707.3291 containing new and improved analysis of counterexamples. 17 page

Resonant leptogenesis in a predictive SO(10) grand unified model

An SO(10) grand unified model considered previously by the authors featuring lopsided down quark and charged lepton mass matrices is successfully predictive and requires that the lightest two right-handed Majorana neutrinons be nearly degenerate in order to obtain the LMA solar neutrino solution. Here we use this model to test its predictions for baryogenesis through resonant-enhanced leptogenesis. With the conventional type I seesaw mechanism, the best predictions for baryogenesis appear to fall a factor of three short of the observed value. However, with a proposed type III seesaw mechanism leading to three pairs of massive pseudo-Dirac neutrinos, resonant leptogenesis is decoupled from the neutrino mass and mixing issues with successful baryogenesis easily obtained.Comment: 22 pages including 1 figure; published version with reference adde

Maximally-localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally-localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization.Comment: 13 pages, with 9 postscript figures embedded. Uses REVTEX and epsf macro

Evidence that the Bursting Component of the X-ray Radiation From 3C 111 Originates in the PC-Scale Jet

Evidence is presented indicating that the bursting component of the X-ray radiation detected in the nuclear region of the active radio galaxy 3C 111 comes from the blobs ejected in the pc-scale jet and not from the accretion disc. After each new outburst the radio flux density associated with it increases to a peak in ~1 year and then subsides over a period of 1-2 years with the flux falling off exponentially as the blob moves outward and dissipates. Similar peaks (bursts) are seen in the X-ray light curve and a cross-correlation between the two shows a very high correlation with the X-ray peaks leading the radio peaks by ~100 days. A second cross-correlation, this time between the radio event start times and the X-ray light curve, also shows a significant correlation. When this is taken together with the long (~1 yr) delay between the start of each ejection event and its associated X-ray peak it indicates that this bursting component of the X-ray flux must be associated with the ejected blobs in the pc-scale jet and not with the accretion disc. Because X-ray telescopes do not have the resolution required to resolve the accretion disc area from the pc-scale jet, this paper is the first to present observational evidence that can pinpoint the point of origin of at least those long-timescale X-ray bursts with durations of 1-3 yrs.Comment: 11 pages, 8 Figures. Accepted for publication in Astrophysics and Space Scienc