Remark on Entropic Characterization of Quantum Operations

In the present paper, the reduction of some proofs in \cite{Roga1} is presented. An entropic inequality for quantum state and bi-stochastic CP super-operators is conjectured.Comment: 5 pages, LaTeX. A conjecture for some entropic inequality is adde

Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we exactly solve the dynamic behaviors of a driven and damped parametric oscillator to obtain the optimal solutions by means of invariant parameters of $K$s to combine with Lewis-Riesenfeld invariant method. This approach can discriminate the external dynamics from the internal evolution of a wave packet by producing independent parametric equations that dramatically facilitate the parametric control on the quantum state evolution in a dissipative system. In order to show the advantages of this method, several time-dependent models proposed in the quantum control field are analyzed in details.Comment: 31 pages, 14 figure

Conditional mutual information and self-commutator

A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain.Comment: LaTex, 9 pages. Minor modifications are made. Any comments are welcome

Remark on the coherent information saturating its upper bound

Coherent information is a useful concept in quantum information theory. It connects with other notions in data processing. In this short remark, we discuss the coherent information saturating its upper bound. A necessary and sufficient condition for this saturation is derived.Comment: 7 pages, LaTeX, a little remark is adde

Matrix integrals over unitary groups: An application of Schur-Weyl duality

The integral formulae over the unitary group \unitary{d} are reviewed with new results and new proofs. The normalization and the bi-invariance of the uniform Haar measure play the key role for these computations. These facts are based on Schur-Weyl duality, a powerful tool from representation theory of group.Comment: v1: 42 pages, LaTeX, no figures. Any comments are welcome! v2: 52 pages, LaTeX, no figures. A new section added. Appendix is also modified. v3: 53 pages, LaTeX, no figures. A conjecture proposed in the first version is cracked in this version. v4: 61 pages, LaTex, no figures; several examples and new propositions are included. v5: 63 pages, some materials are added. arXiv admin note: text overlap with arXiv:quant-ph/0512255 by other author

Average coherence and its typicality for random mixed quantum states

Wishart ensemble is a useful and important random matrix model used in diverse fields. By realizing induced random mixed quantum states as Wishart ensemble with the fixed-trace one, using matrix integral technique we give a fast track to the average coherence for random mixed quantum states induced via partial-tracing of the Haar-distributed bipartite pure states. As a direct consequence of this result, we get a compact formula of the average subentropy of random mixed states. These obtained compact formulae extend our previous work.Comment: v2: 18 pages, minor errors and misprints are corrected, final version, accepted for publication in J. Phys. A; v1: 17 pages, LaTeX, no figures. Any comments are welcome

Dirac Delta Function of Matrix Argument

Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed knowledge about Heaviside unit step function and Dirac delta function. Then its extensions of Dirac delta function to vector spaces and matrix spaces are discussed systematically, respectively. The detailed and elementary proofs of these results are provided. Though we have not seen these results formulated in the literature, there certainly are predecessors. Applications are also mentioned.Comment: 26 pages, LaTeX, no figures. Any comments are welcome!. arXiv admin note: text overlap with arXiv:quant-ph/0012101 by other author

An Efficient Approach for Cell Segmentation in Phase Contrast Microscopy Images

In this paper, we propose a new model to segment cells in phase contrast microscopy images. Cell images collected from the similar scenario share a similar background. Inspired by this, we separate cells from the background in images by formulating the problem as a low-rank and structured sparse matrix decomposition problem. Then, we propose the inverse diffraction pattern filtering method to further segment individual cells in the images. This is a deconvolution process that has a much lower computational complexity when compared to the other restoration methods. Experiments demonstrate the effectiveness of the proposed model when it is compared with recent works

Vertex tensor category structure on a category of Kazhdan--Lusztig

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic tensor product theory for generalized modules for a vertex operator algebra developed by Huang, Lepowsky and the author. We do this by proving that the conditions for applying this general logarithmic tensor product theory hold. As a consequence, we prove that this category has a natural vertex tensor category structure, and in particular we obtain a new, vertex-algebraic, construction of the natural associativity isomorphisms and proof of their properties.Comment: 20 page

On some entropy inequalities

In this short report, we give some new entropy inequalities based on R\'{e}nyi relative entropy and the observation made by Berta {\em et al} [arXiv:1403.6102]. These inequalities obtained extends some well-known entropy inequalities. We also obtain a condition under which a tripartite operator becomes a Markov state.Comment: 7 pages, LaTeX, any comments are welcome