Exact dynamics of concurrence-based entanglement in a system of four spin-1/2 particles on a triangular ladder structure

TL;DR

This paper derives exact dynamics of entanglement in a four-qubit triangular spin ladder with XX and Dzyaloshinskii-Moriya interactions, highlighting conditions for W state generation and entanglement transfer.

Contribution

It provides an exact analytical description of concurrence dynamics and the relationship between system parameters and W state formation in a four-qubit triangular ladder.

Findings

W states are generated during evolution with equal pairwise concurrence.

Maximum entanglement occurs when xx and yy correlations are maximized.

zz correlations suppress entanglement in W states.

Abstract

Motivated by the ability of triangular spin ladders to implement quantum information processing, we propose a type of such systems whose Hamiltonian includes the XX Heisenberg interaction on the rungs and DzyaloshinskiiMoriya (DM) coupling over the legs. In this work, we discuss how tuning the magnetic interactions between elements of a nanomagnetic cell of a triangular ladder which contains four qubits influences on the dynamical behavior of entanglement shared between any pairs of the system. In this work, we make use of concurrence for monitoring entanglement. It is realized that the generation of quantum W states is an important feature of the present model when the system evolves unitarily with time. In general, coincidence with the emergence of W states, the concurrences of all pairs are equal to $N/2$, where N is the number of system's qubits. We also obtain the precise relationship between the incidence of such states and the value of DM interaction as well as the time of entanglement transfer. Finally, by studying the two-point quantum correlations and expectation values of different spin variables, we find that xx and yy correlations bring the entanglement to a maximum value for W states, whereas for these states, zz correlation between any pairs completely quenches. Our results reveal that although $S^{tot}_{z}$ does not commute with the system's Hamiltonian, its expectation value remains constant during time evolution which is a generic property of quantum W states.