Inequalities for purity parameters for multipartite and single qudit states

Abstract

We analyze a recently found inequality for eigenvalues of the density matrix and purity parameter describing either a bipartite system state or a single qudit state. The Minkowski type trace inequality for the density matrices of the qudit states is rewritten in terms of the purities. The properties of the obtained inequality are discussed. The $X$-states of the two qubits and the single qudit are considered in detail. A study of the relation of the obtained purity inequalities with the entanglement is presented.

arXiv comment9 pages, 7 figures

References in corpus (7)

• Separability Criterion for Density Matrices
• A simple test for hidden variables in spin-1 system
• Quantum strong subadditivity condition for systems without subsystems
• Generalized qubit portrait of the qutrit state density matrix
• Separability and entanglement of the qudit X-state with j = 3/2
• Evidence that All States Are Unitarily Equivalent to X States of the Same Entanglement
• New Minkowski type inequalities and entropic inequalities for quantum states of qudits