We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, X states. An expression for the trace distance coherence for all pure states and a semi definite program for arbitrary states is provided. We also explore the relation between l1-norm and relative entropy based measures of coherence, and give a sharp inequality connecting the two. In addition, it...

In this paper, we focus on the weighted Bergman spaces Aφp in D with φ∈W0. We first give characterizations of those finite positive Borel measures µ such that embedding Aφp⊂Lμq is bounded or compact for 0<p,q<∞. Then describe Toeplitz operators Tμ from one space to another Aφq all possible Finally, characterize Schatten class Aφ2.

Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm minimization (NNM) as a convex relaxation of the nonconvex rank minimization. However, NNM tends to over-shrink the rank components and treats the different rank com...

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output Rényi entropies. We show that random channels obtained by randomly coupling the inpu...

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation EF and the conjugate function E of the entanglement function E(ρ) = S(TrA ρ). We then consider the conjectured strong superadditivity of the entanglement of formation EF (ρ) ≥ EF (ρI) + EF (ρII), where ρI and ρII are the reductions of ρ to the different Hilbert space copies, and prov...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

Two–sided estimates of Schatten–von Neumann norms for weighted Volterra integral operators are established. Analogous problems for some potential-type operators defined on R are solved. Let H be a separable Hilbert space and let σ∞(H) be the class of all compact operators T : H → H, which forms an ideal in the normed algebra B of all bounded linear operators onH. To construct a Schattenvon Neum...