Deriving Entropic Inequalities for Two Coupled Superconducting Circuits

TL;DR

This paper investigates entropic inequalities in two coupled superconducting circuits, analyzing their quantum information properties through perturbation methods and thermal states, with implications for quantum computing systems.

Contribution

It introduces a method to derive entropic inequalities for coupled superconducting circuits using parametric excitation and thermal state analysis.

Findings

Subadditivity condition holds for von Neumann and deformed entropies.

Mutual information varies with temperature, indicating thermal effects on quantum correlations.

Approach applicable to harmonic oscillator models of coupled qubits.

Abstract

We discuss the known construction of two interacting superconducting circuits, based on Josephson junctions, that can be precisely engineered and easily controlled. In particular, we use the parametric excitation of two circuits, realized by an instant change of the qubit coupling, to study entropic and information properties of the density matrix of the composite system. The density matrix is obtained from the initial thermal state and is then analyzed in the approximation of small perturbation parameter and sufficiently low temperature. We also check the subadditivity condition for this system both for von Neumann and deformed entropies and look at the dependance of mutual information on the temperature of the system. Finally, we discuss the applicability of this approach to describe such system of two coupled superconducting qubits as harmonic oscillators with limited Hilbert space.