Entropic and Information Inequalities for Indivisible Qudit Systems*

Igor Ya. Doskoch, Margarita A. Man’ko

Vladimir I. Man’ko, Z. Seilov

Vladimir I. Man’ko, Taiman T. Sabyrgaliyev

Margarita A. Man’ko, Vladimir I. Man’ko

We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki-Lieb inequality, which characterize hidden quantum correlations of observables associated with these indivisible systems. We derive these relations employing a specific map of the entropic inequalities known for density matrices of multiqudit systems to the inequalities for density matrices of single-qudit systems. We present the obtained relations in the form of mathematical inequalities for arbitrary Hermitian N × N -matrices. We consider examples of superconducting qubits and qudits. We discuss the hidden correlations in single- qudit states as a new resource for quantum technologies analogous to the known resource in correlations associated with the entanglement in multiqudit systems.

Margarita A. Man’ko, Vladimir I. Man’ko

We discuss the notion of hidden correlations in classical and quantum indivisible systems along with such characteristics of the correlations as the mutual information and conditional information corresponding to the entropic subadditivity condition and the entropic strong subadditivity condition. We present an analog of the Bayes formula for systems without subsystems, study entropic inequality for von Neumann entropy and Tsallis entropy of the single-qudit state, and discuss the inequalities for qubit and qutrit states as an example.

Julio A. López-Saldívar, Octavio Castaños, Margarita A. Man’ko +1 more