Identification of a natural fieldlike entanglement resource in trapped-ion chains

The electromagnetic trapping of ion chains can be regarded as a process of nontrivial entangled quantum state preparation within Hilbert spaces of the local axial motional modes. To begin uncovering properties of this entanglement resource produced as a by-product of conventional ion-trap quantum information processing, the quantum continuous-variable formalism is herein utilized to focus on the leading-order entangled ground state of local motional modes in the presence of a quadratic trapping potential. The decay of entanglement between disjoint subsets of local modes is found to exhibit features of entanglement structure and responses to partial measurement reminiscent of the free massless scalar field vacuum. With significant fidelities between the two, even for large system sizes, a framework is established for initializing quantum field simulations by "imaging" extended entangled states from natural sources, rather than building correlations through deep circuits of few-body entangling operators. By calculating probabilities in discrete Fock subspaces of the local motional modes, we present considerations for locally transferring these predistributed entanglement resources to the qudits of ion internal energy levels, improving this procedure's anticipated experimental viability.