Kraus operators for a pair of interacting qubits: a case study

TL;DR

This paper derives the Kraus operators for a pair of interacting qubits with arbitrary interaction strength, including measurement effects, and analyzes how entanglement dynamics depend on interaction strength.

Contribution

It provides the first explicit derivation of Kraus operators for two interacting qubits with measurement, enabling detailed analysis of entanglement evolution.

Findings

Stronger inter-qubit interaction prolongs entanglement.

Derived Kraus operators facilitate understanding of two-qubit open system dynamics.

Finite-time entanglement loss observed depending on interaction strength.

Abstract

The Kraus form of the completely positive dynamical maps is appealing from the mathematical and the point of the diverse applications of the open quantum systems theory. Unfortunately, the Kraus operators are poorly known for the two-qubit processes. In this paper, we derive the Kraus operators for a pair of interacting qubit, while the strength of the interaction is arbitrary. One of the qubits is subjected to the x-projection spin measurement. The obtained results are applied to calculate the dynamics of the initial entanglement in the qubits system. We obtain the loss of the correlations in the finite time interval; the stronger the inter-qubit interaction, the longer lasting entanglement in the system.