Hidden Quantum Correlations in Single Qudit Systems†

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

Margarita A. Man’ko

Igor Ya. Doskoch, Margarita A. Man’ko

I. A. Silva, Diogo de Oliveira Soares Pinto, Eduardo Ribeiro de Azevêdo

Margarita A. Man’ko

We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in the state of a single qudit. We consider analogs of the entanglement phenomena in the systems without subsystems related to strong hidden quantum correlations.

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.