Inequalities for Purity Parameters of Multiqudit and Single-Qudit States

摘要

We analyze the recently found inequality for eigenvalues of the density matrix and purity parameters describing either a bipartite-system state or a single-qudit state. We rewrite the Minkowski-type trace inequality for the density matrices of the qudit states in terms of the purity parameters and discuss the properties of the inequality obtained, paying special attention to the X-states of two qubits and a single qudit. Also we study the relation of the purity inequalities obtained with the entanglement.