Hidden correlations in indivisible qudits as a resource for quantum technologies on examples of superconducting circuits

TL;DR

This paper demonstrates that indivisible qudit systems exhibit hidden quantum correlations satisfying entropic inequalities, which can serve as a new resource for quantum technologies, exemplified through superconducting circuits.

Contribution

It introduces a method to identify and analyze hidden correlations in single-qudit systems using entropic inequalities, expanding the understanding of quantum resources beyond entanglement.

Findings

Hidden correlations satisfy entropic and information inequalities.

Relations are applicable to arbitrary Hermitian matrices.

Examples include superconducting qubits and qudits.

Abstract

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 NxN-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.