Partitioned trace distances

New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar properties to the standard trace distance, including the unitary invariance, the strong convexity and the close relations to the classical distances. The partitioned distances cannot increase under quantum operations of certain kind including bistochastic maps. All the basic properties are re-formulated as majorization relations. Possible applications to quantum information processing are briefly discussed.Comment: 8 pages, no figures. Significant changes are made. New section on majorization is added. Theorem 4.1 is extended. The bibliography is enlarged

Notes on entropic characteristics of quantum channels

One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss few channel characteristics expressed by means of generalized entropies. Such characteristics can often be dealt in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the $q$-average output entropy of degree $q\geq1$ is bounded from above by the $q$-entropy of the input density matrix. Concavity properties of the $(q,s)$-entropy exchange are considered. Fano type quantum bounds on the $(q,s)$-entropy exchange are derived. We also give upper bounds on the map $(q,s)$-entropies in terms of the output entropy, corresponding to the completely mixed input.Comment: 10 pages, no figures. The statement of Proposition 1 is explicitly illustrated with the depolarizing channel. The bibliography is extended and updated. More explanations. To be published in Cent. Eur. J. Phy

Supersymmetry and Gauge Invariance Constraints in a U(1)×\times U(1)′^{\prime }-Higgs Superconducting Cosmic String Model

A supersymmetric extension of the $U(1)\times U(1)^{\prime }$-Higgs bosonic superconducting cosmic string model is considered,and the constraints imposed upon such a model due to renormalizability, supersymmetry, and gauge invariance are examined. For a simple model with a single $U(1)$ chiral superfield and a single $$ chiral superfield, the Witten mechanism for bosonic superconductivity (giving rise to long range gauge fields outside of the string) does not exist. The simplest model that can accommodate the requisite interactions requires five chiral supermultiplets. This superconducting cosmic string solution is investigated.Comment: 17 pages, revtex, no figures; to appear in Phys. Rev.

Relations for certain symmetric norms and anti-norms before and after partial trace

Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined. The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases. The obtained results concern operators acting on the tensor product of two finite-dimensional Hilbert spaces. For any such operator, we obtain upper bounds on norms of its partial trace in terms of the corresponding dimensionality and norms of this operator. Similar inequalities, but in the opposite direction, are obtained for certain anti-norms of positive matrices. Through the Stinespring representation, the results are put in the context of trace-preserving completely positive maps. We also derive inequalities between the unified entropies of a composite quantum system and one of its subsystems, where traced-out dimensionality is involved as well.Comment: 11 pages, no figures. A typo error in Eq. (5.15) is corrected. Minor improvements. J. Stat. Phys. (in press

Continuity and Stability of Partial Entropic Sums

Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann's partial fidelities.Comment: 9 pages, no figures. Some explanatory and technical improvements are made. The bibliography is extended. Detected errors and typos are correcte

An adaptive autoregressive pre-whitener for speech and acoustic signals based on parametric NMF

A common assumption in many speech and acoustic processing methods is that the noise is white and Gaussian (WGN). Although making this assumption results in simple and computationally attractive methods, the assumption is often too simple and crude in many applications. In this paper, we introduce a general purpose and online pre-whitener which can be used as a pre-processor with methods based on the WGN assumption, improving their reliability and performance in applications with colored noise. The pre-whitener is a time-varying filter whose coefficients are found using a parametric non-negative matrix factorization (NMF), based on autoregressive (AR) mixture modeling of both the noise component and the signal component constituting the noisy signal. Compared to other types of pre-whiteners, we show that the proposed pre-whitener has the best performance, especially in applications with non-stationary noise. We also perform a large number of experiments to quantify the benefits of using a pre-whitener as a pre-processor for methods based on the WGN-assumption. The applications of interest were pitch estimation and time-of-arrival (TOA) estimation, where the WGN assumption is very popular

The normative underpinnings of population-level alcohol use: An individual-level simulation model

Background. By defining what is “normal,” appropriate, expected, and unacceptable, social norms shape human behavior. However, the individual-level mechanisms through which social norms impact population-level trends in health-relevant behaviors are not well understood. Aims. To test the ability of social norms mechanisms to predict changes in population-level drinking patterns. Method. An individual-level model was developed to simulate dynamic normative mechanisms and behavioral rules underlying drinking behavior over time. The model encompassed descriptive and injunctive drinking norms and their impact on frequency and quantity of alcohol use. A microsynthesis initialized in 1979 was used as a demographically representative synthetic U.S. population. Three experiments were performed in order to test the modelled normative mechanisms. Results. Overall, the experiments showed limited influence of normative interventions on population-level alcohol use. An increase in the desire to drink led to the most meaningful changes in the population’s drinking behavior. The findings of the experiments underline the importance of autonomy, that is, the degree to which an individual is susceptible to normative influence. Conclusion. The model was able to predict theoretically plausible changes in drinking patterns at the population level through the impact of social mechanisms. Future applications of the model could be used to plan norms interventions pertaining to alcohol use as well as other health behaviors

Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy

We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two entropies which are due to the fact that the Brownian particle and its environment are entangled. We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic properties, as it is the case for the Landauer principle.Comment: 8 pages, 7 figure

On Effective Theory of Brane World with Small Tension

The five dimensional theory compactified on $S^1$ with two ``branes'' (two domain walls) embedded in it is constructed, based on the field-theoretic mechanism to generate the ``brane''. Some light states localized in the ``brane'' appear in the theory. One is the Nambu-Goldstone boson, which corresponds to the breaking of the translational invariance in the transverse direction of the ``brane''. In addition, if the tension of the ``brane'' is smaller than the fundamental scale of the original theory, it is found that there may exist not only massless states but also some massive states lighter than the fundamental scale in the ``brane''. We analyze the four dimensional effective theory by integrating out the freedom of the fifth dimension. We show that some effective couplings can be explicitly calculated. As one of our results, some effective couplings of the state localized in the ``brane'' to the higher Kaluza-Klein modes in the bulk are found to be suppressed by the width of the ``brane''. The resultant suppression factor can be quantitatively different from the one analyzed by Bando et al. using the Nambu-Goto action, while they are qualitatively the same.Comment: 17 pages, uses REVTEX macr