Related papers: A generalized skew information and uncertainty rel…
In order to study the communication between information systems, Gong and Xiao [Z. Gong and Z. Xiao, Communicating between information systems based on including degrees, International Journal of General Systems 39 (2010) 189--206] proposed…
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.
This note explores uncertainty inequalities for quantum analogues of the Fisher information including the Wigner-Yanase skew information, and their connection to the quantum Sobolev inequalities proved by the author in [Journal of…
The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
Several generalizations of the logistic distribution, and certain related models, are proposed by many authors for modeling various random phenomena such as those encountered in data engineering, pattern recognition, and reliability…
In this work, we derive state-dependent uncertainty relations (uncertainty equalities) in which commutators of incompatible operators (not necessarily Hermitian) are explicitly present and state-independent uncertainty relations based on…
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and…
In this paper we have introduced a generalized version of alpha beta skew normal distribution in the same line of Sharafi et al. (2017) and investigated some of its basic properties. The extensions of the proposed distribution have also…
We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces, and then provide a unified extension of the recent…
We describe an error in the proof of a key proposition, which was necessary for the proof of the main result. Alternate proofs of the main result are given by Ozsvath-Stipsicz-Szabo and Dai-Hom-Stoffregen-Truong.
For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…
Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information…
This note reports partial results related to the Gaussian product inequality (GPI) conjecture for the joint distribution of traces of Wishart matrices. In particular, several GPI-related results from Wei (2014) and Liu et al. (2015) are…
In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove results on…
A recent paper [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of…
In this paper, we give a Schr\"odinger-type uncertainty relation using the Wigner-Yanase-Dyson skew information. In addition, we give Schr\"odinger-type uncertainty relation by use of a two-parameter extended correlation measure. Moreover,…
In this paper we give a generalization of a result of Wei.
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…