Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Abstract: In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.

Conformable integral version of Hermite-Hadamard-Fejér inequalities via η -convex functions

Abstract: The purpose of the article is to use symmetric η-convex functions to develop Hermite-Hadamard-Fejer inequality for conformable integral. We establish several conformable integral versions of Hermite-Hadamard-Fejer type inequality for the η-convex functions by use of an identity linked with Hermite-Hadamard inequality.

Hadamard quantum broadcast channels

Abstract: We consider three different communication tasks for quantum broadcast channels, and we determine the capacity region of a Hadamard broadcast channel for these various tasks. We define a Hadamard broadcast channel to be such that the channel from the sender to one of the receivers is entanglement-breaking and the channel from the sender to the other receiver is complementary to this one. As such, this channel is a quantum generalization of a degraded broadcast channel, which is well known in classical information theory. The first communication task we consider is classical communication to both receivers, the second is quantum communication to the stronger receiver and classical communication to other, and the third is entanglement-assisted classical communication to the stronger receiver and unassisted classical communication to the other. The structure of a Hadamard broadcast channel plays a critical role in our analysis: The channel to the weaker receiver can be simulated by performing a measurement channel on the stronger receiver’s system, followed by a preparation channel. As such, we can incorporate the classical output of the measurement channel as an auxiliary variable and solve all three of the above capacities for Hadamard broadcast channels, in this way avoiding known difficulties associated with quantum auxiliary variables.

Mutually unbiased triplets from non-affine families of complex Hadamard matrices in dimension six

Abstract: We study the problem of constructing mutually unbiased bases in dimension six. This approach is based on an efficient numerical method designed to find solutions to the quantum state reconstruction problem in finite dimensions. Our technique suggests the existence of previously unknown symmetries in Karlsson's non-affine family $K_6^{(2)}$ which we confirm analytically. Also, we obtain strong evidence that no more than three mutually unbiased bases can be constructed from pairs which contain members of some non-affine families of complex Hadamard matrices.

On the zero point problem of monotone operators in Hadamard spaces

Abstract: In this paper, by using products of finitely many resolvents of monotone operators, we propose an iterative algorithm for finding a common zero of a finite family of monotone operators and a common fixed point of an infinitely countable family of nonexpansive mappings in Hadamard spaces. We derive the strong convergence of the proposed algorithm under appropriate conditions. A common fixed point of an infinitely countable family of quasi-nonexpansive mappings and a common zero of a finite family of monotone operators are also approximated in reflexive Hadamard spaces. In addition, we define a norm on X◇ := spanX∗ and give an application of this norm, where X is an Hadamard space with dual space X∗. A numerical example to solve a nonconvex optimization problem will be exhibited in an Hadamard space to support our main results.