Entanglement formation under random interactions

TL;DR

This paper investigates how entanglement between two qubits evolves under different types of random interactions, combining analytical and numerical methods to understand the dynamics.

Contribution

It provides a novel analysis of entanglement formation under both static and fluctuating random Hamiltonians, including geometric insights into SU(4).

Findings

Entanglement dynamics depend on the type of randomness in interactions.

Derived metric tensor and Laplace-Beltrami for SU(4).

Identified differences between static and fluctuating Hamiltonian cases.

Abstract

The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with randomly chosen but time-independent interaction Hamiltonians. Secondly we consider the case of a temporally fluctuating Hamiltonian, where the unitary evolution can be understood as a random walk on the SU (4) group manifold. As a by-product we compute the metric tensor and its inverse as well as the Laplace-Beltrami for SU (4).