Abstract
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.
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Man’ko, V.I., Markovich, L.A. Inequalities for Purity Parameters of Multiqudit and Single-Qudit States. J Russ Laser Res 37, 133–140 (2016). https://doi.org/10.1007/s10946-016-9553-0
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DOI: https://doi.org/10.1007/s10946-016-9553-0