Natalie Klco

The reduction and distortion of quantum correlations in the presence of classical noise leads to varied levels of inefficiency in the availability of entanglement as a resource for quantum information processing protocols. While generically minimizing required entanglement for mixed quantum states remains challenging, a class of many-body Gaussian quantum states ($\mathcal{N}$IC) is here identified that exhibits two-mode bipartite entanglement structure, resembling that of pure states, for which the logarithmic negativity entanglement measure remains invariant upon inclusion of the classical correlations and optimal entanglement resources can be clearly quantified. This subclass is found to be embedded within a broader class of many-body Gaussian states ($\mathcal{N}$-SOL) that retain two-mode entanglement structure for detection processes. These two entanglement classes are relevant in theoretical and experimental applications from the scalar field vacuum to the local axial motional modes of trapped ion chains. Utilizing the subspace that heralds inseparability in response to partial transposition, a minimum noise filtering process is designed to be necessary, sufficient, and computable for determining membership in these classes of entanglement structure. Application of this process to spacelike regions of the free scalar field vacuum is found to improve resource upper bounds, providing new understanding of the entanglement required for the quantum simulation of quantum fields as observed by arrays of local detectors.

The electromagnetic trapping of ion chains can be regarded as a process of non-trivial entangled quantum state preparation within Hilbert spaces of the local axial motional modes. To begin uncovering properties of this entanglement resource produced as a byproduct 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 via "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, considerations are presented for locally transferring these pre-distributed entanglement resources to the qudits of ion internal energy levels, improving this procedure's anticipated experimental viability.