Trace inequalities on a generalized Wigner-Yanase skew information

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixure. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued

Fundamental properties of Tsallis relative entropy

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible. The generalized Tsallis relative entropy is defined and its subadditivity is shown by its joint convexity. Moreover, the generalized Peierls-Bogoliubov inequality is also proven

Quantum linear mutual information and classical correlations in globally pure bipartite systems

We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information is introduced and the two quantities are compared for a system of oscillators coupled with both linear and non-linear interactions. The classical correlations help to understand how much of the quantum loss of purity are due to intrinsic quantum effects and how much is related to the probabilistic character of the initial states, a characteristic shared by both the classical and quantum pictures. Our examples show that, for initially localized Gaussian states, the classical statistical mutual linear entropy follows its quantum counterpart for short times. For non-Gaussian states the behavior of the classical and quantum measures of information are still qualitatively similar, although the fingerprints of the non-classical nature of the initial state can be observed in their different amplitudes of oscillation.Comment: (16 pages, 4 figures

Parametrization of projector-based witnesses for bipartite systems

Entanglement witnesses are nonpositive Hermitian operators which can detect the presence of entanglement. In this paper, we provide a general parametrization for orthonormal basis of ${\mathbb C}^n$ and use it to construct projector-based witness operators for entanglement detection in the vicinity of pure bipartite states. Our method to parameterize entanglement witnesses is operationally simple and could be used for doing symbolic and numerical calculations. As an example we use the method for detecting entanglement between an atom and the single mode of quantized field, described by the Jaynes-Cummings model. We also compare the detection of witnesses with the negativity of the state, and show that in the vicinity of pure stats such constructed witnesses able to detect entanglement of the state.Comment: 12 pages, four figure

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

Heat transfer and solidification processes of alloy melt with undercooling—Part II: Solidification model

The solidification process of undercooled alloy melts has been clarified experimentally in Part I of this paper. In the present paper, using the experimental evidence, a solidification model linking macroscopic heat transfer and microscopic solidification is presented. The model reflects the microscopic solidification phenomena occurring until the thermodynamically unstable field shifts to equilibrium, consisting of three fundamental processes: (first stage) free growth, (second stage) crystal expansion with relaxation, and (third stage) equilibrium solidification. Based on this model, a numerical simulation is carried out for the temperature change, interface movement, and solute concentration distribution during the solidification of an undercooled Bi-Sn melt. Theoretical predictions of the temperature changes involving the recalescence, terminal time of the relaxation process, and microsegregation for the solidified texture agree quantitatively with experimental observations. © 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Heat transfer and solidification processes of alloy melt with undercooling—Part I: Experimental results

The solidification process of Pb-Sn and Bi-Sn alloy melts is discussed to obtain a basic understanding of the essential phenomena of solidification with undercooling. First, from macroscopic observations, it is shown that the solidification process consists of the following three stages: (1) free growth with recalescence dissipation of thermal undercooling, (2) expansion of crystals with the relaxation of constitutional undercooling or with the recovering process of interrupted quasi-steady heat conduction, and (3) equilibrium solidification. The specific features of free growth under non-uniform undercooling are also shown by comparison with the Lipton, Glicksman, and Kurz model. Next, from microscopic observations, the distribution of the solute concentration and the change of crystal morphology in the solidified materials were investigated quantitatively using scanning electron microscopy and energy-dispersive spectroscopy. Finally, the solidification path during the above three fundamental processes is dynamically represented on phase diagrams. © 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

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