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

On the topological reduction from the affine to the orthogonal gauge theory of gravity

Making use of the fibre bundle theory to describe metric-affine gauge theories of gravity we are able to show that metric-affine gauge theory can be reduced to the Riemann-Cartan one. The price we pay for simplifying the geometry is the presence of matter fields associated with the nonmetric degrees of freedom of the original setup. Also, a possible framework for the construction of a quantum gravity theory is developed along the text.Comment: 22 pages, no figures. V2: Title changed, Small changes on the text, references added. Final version to appear in Journal Of Geometry and Physic

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

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem

The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to O(d)-covariant channels this leads to a complete characterization and reveals a remarkable feature: instances of channels which are not in the convex hull of unitaries can return to it when either taking finitely many copies of them or supplementing with a completely depolarizing channel. In these scenarios this implies that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

Monetary Policy Rules and Directions of Causality: a Test for the Euro Area

Using a VAR model in first differences with quarterly data for the euro zone, the study aims to ascertain whether decisions on monetary policy can be interpreted in terms of a “monetary policy rule” with specific reference to the so-called nominal GDP targeting rule (Hall and Mankiw, 1994; McCallum, 1988; Woodford, 2012). The results obtained indicate a causal relation proceeding from deviation between the growth rates of nominal gross domestic product (GDP) and target GDP to variation in the three-month market interest rate. The same analyses do not, however, appear to confirm the existence of a significant inverse causal relation from variation in the market interest rate to deviation between the nominal and target GDP growth rates. Similar results were obtained on replacing the market interest rate with the European Central Bank refinancing interest rate. This confirmation of only one of the two directions of causality does not support an interpretation of monetary policy based on the nominal GDP targeting rule and gives rise to doubt in more general terms as to the applicability of the Taylor rule and all the conventional rules of monetary policy to the case in question. The results appear instead to be more in line with other possible approaches, such as those based on post Keynesian analyses of monetary theory and policy and more specifically the so-called solvency rule (Brancaccio and Fontana, 2013, 2015). These lines of research challenge the simplistic argument that the scope of monetary policy consists in the stabilization of inflation, real GDP, or nominal income around a “natural equilibrium” level. Rather, they suggest that central banks actually follow a more complex purpose, which is the political regulation of the financial system with particular reference to the relations between creditors and debtors and the related solvency of economic units

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

Solar photo-Fenton at mild conditions to treat a mixture of six emerging pollutants

The applicability of photo-Fenton to degrade a mixture of emerging pollutants (EPs) namely amoxycillin, acetaminophen, acetemiprid, caffeine, clofibric acid and carbamazepine has been studied at different scenarios. At high concentrations, acidic photo-Fenton was able to achieve a fast removal of the EPs. Although, complete mineralization was not reached, the toxicity of the solution was decreased according to the respiration of activated sludge and luminescence of Vibrio fischeri assays, although according to this last assay a transitory enhancement of the toxicity was found, attributable to the formation of toxic byproducts such as phenols, chlorophenols and chlorinated pyrydines. Experiments carried out with 5 mg/l of each EP showed that at neutral media the process was two orders of magnitude less efficient than at acidic pH, although it was still able to remove the EPs. The aqueous matrix has a remarkable effect on the process as the presence of humic acids increased the reaction rate and inorganic salts played an inhibitory role. Finally, experiments performed with 10 lg/l of each EP showed that under those experimental conditions nearly complete removal of the EPs was reached with neutral photo-Fenton after 120 min of irradiation; in this case, humic substances played a disfavorable role.We want to thank the financial support of Spanish Ministerio de Ciencia e Innovacion (CTQ 2009-13459-0O5-03) and (CTQ 2009-3459-C05-01).Bernabeu García, A.; Palacios Guillem, S.; Vicente Candela, R.; Vercher Pérez, RF.; Malato Rodríguez, S.; Arques Sanz, A.; Amat Payá, AM. (2012). Solar photo-Fenton at mild conditions to treat a mixture of six emerging pollutants. Chemical Engineering Journal. 198:65-72. https://doi.org/10.1016/j.cej.2012.05.056S657219

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole's accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a_* of the black hole (|a_*| < 1). The ten spins that have so far been measured by this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2, 6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405) who find no evidence for a correlation between the power of ballistic jets and black hole spi