Entanglement statistics of randomly interacting spins

TL;DR

This paper studies how the entanglement in the ground states of small quantum systems varies with interaction types and strengths, revealing the influence of interaction topology on entanglement patterns.

Contribution

It introduces a detailed analysis of entanglement behavior in multi-qubit systems with random and deterministic interactions, highlighting the role of interaction topology.

Findings

Entanglement varies continuously with interaction strength.

GHZ entanglement is favored by non-separable collective interactions.

Separable pairwise interactions lead to ground states near W states.

Abstract

We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can continuously interpolate between deterministic separable eigenstates and fully random entangled eigenstates, with non-trivial intermediate behavior. Entanglement strongly depends on the underlying topology of the interaction among the qubits. For a certain class of interactions GHZ entanglement is favoured by a non-separable collective interaction, while for fully separable pairwise interactions the ground states concentrate in the vicinity of W states.