  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.
