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We obtain a new matrix inequality for an arbitrary density matrix of composite/noncomposite qudit systems including a single-qudit state. For bipartite systems, this inequality coincides with a known entropic inequality like the subadditivity condition. The examples of two-qubit system and qudit with j = 3 /2 are discussed. [ABSTRACT FROM AUTHOR]

Using the monotonicity of relative entropy of composite quantum systems, we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Examples of qutrit state inequalities and the 'qubit portrait' bound for the distance between the qutrit states are considered in explicit form. [ABSTRACT FROM AUTHOR]

Abstract: In an earlier paper Srivastava [2005. Combinatorial Hermitian Algebras Derived from Latin Squares. J. Statist. Plann. Inference 129, 305–316], subsequently referred to as [S05], the author had presented an infinite class of algebras of Hermitian matrices. Each of these algebras were derived from Latin Squares. In this paper, we show how to obtain a unitary matrix (over the complex field) such that is a diagonal matrix, for all matrices belonging to a particular algebra. The notation is defined in the next paragraph. The said diagonal matrix is a matrix that contains the characteristic roots of . The matrix may be different for different algebras. Many other related results are also presented. The algebras are further discussed. How the Hermitian matrices arise in Quantum Mechanics (where every observable attribute of every physical phenomenon is in a sense characterized by a Hermitian matrix) is briefly described. The significance of the existence of Hermitian algebras and the application to Physics and Chemistry is pointed out. [Copyright &y& Elsevier]

Abstract: This paper presents an infinite class of algebras of Hermitian matrices of size , where n is a positive integer and where is a prime number or a power of a prime number (so that the Galois Field GF exists). For each such n, we obtain separate Hermitian algebras, no two of which mutually commute. [Copyright &y& Elsevier]