Ground-state entanglement in coupled qubits

TL;DR

This paper proves that continuous changes in the ground state of coupled qubits, indicated by shifts in $\sigma_z$ expectation values, imply entanglement, and introduces practical entanglement witnesses based on susceptibilities.

Contribution

It establishes a theoretical link between ground state transformations and entanglement, and develops entanglement witnesses applicable to multi-qubit systems.

Findings

Ground state entanglement is indicated by changes in $\sigma_z$ expectations during Hamiltonian parameter variations.

Introduces entanglement witnesses based on cross-susceptibilities for detecting bipartite and global entanglement.

Connects energy level anticrossings with the presence of ground state entanglement.

Abstract

We study a system of qubits that are coupled to each other via only one degree of freedom represented, e.g., by $\sigma_z$-operators. We prove that, if by changing the Hamiltonian parameters, a non-degenerate ground state of the system is continuously transformed in such a way that the expectation values of $\sigma_z$ operators of at least two coupled qubits change, this ground state is entangled. Using this proof, we discuss connection between energy level anticrossings and ground state entanglement. Following the same line of thought, we introduce entanglement witnesses, based on cross-susceptibilities, that can detect ground state entanglement for any bipartition of the multi-qubit system. A witness for global ground state entanglement is also introduced.