Bloch-sphere approach to correlated noise in coupled qubits

TL;DR

This paper introduces a generalized Bloch vector method to analyze how correlated noise affects decoherence in two interacting qubits, revealing that initial states and Hamiltonian symmetry significantly influence decoherence rates.

Contribution

It develops an analytic framework using a generalized Bloch vector for two-qubit systems to study correlated noise effects on decoherence.

Findings

Decoherence rates depend strongly on initial states and Hamiltonian symmetry.

Correlated noise can either accelerate or slow decoherence depending on system parameters.

The approach provides a geometrical perspective similar to the Bloch sphere for two-qubit systems.

Abstract

By use of a generalized Bloch vector construction, we study the decoherence of a system composed of two interacting qubits in a general noisy environment. In particular, we investigate the effects of correlations in the noise acting on distinct qubits. Our treatment of the two-qubit system by use of the generalized Bloch vector leads to tractable analytic equations for the dynamics of the 4-level Bloch vector and allows for the application of geometrical concepts from the well known 2-level Bloch sphere. We find that in the presence of correlated or anticorrelated noise, the rate of decoherence is very sensitive to the initial two-qubit state, as well as to the symmetry of the Hamiltonian. In the absence of symmetry in the Hamiltonian, correlations only weakly impact the decoherence rate.