Multipartite entanglement of three trapped ions in a cavity and W- State generation

TL;DR

This paper proposes a scheme to generate three-ion W-states in a cavity, analyzing entanglement dynamics and showing reversible entanglement exchange with potential for multipartite quantum information processing.

Contribution

It introduces a novel method for creating three-ion W-states using trapped ions and cavity interactions, with detailed entanglement analysis including negativity measures.

Findings

W-state generation occurs in about 10 microseconds.

Entanglement can be manipulated via initial phonon number.

Reversible entanglement exchange observed among ions and photons.

Abstract

A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with red sideband tuned single mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating three ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 $\mu $ sec. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by appropriate choice of initial state phonon number. The ionic qubits in W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial $K-$way negativities (K=2 to 4) are obtained to study the evolution of entanglement distribution as a function of interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of interaction parameter, the three ions and photon-phonon system are found to have four partite entanglement, generated by 2-way and 3-way correlations.