  Characterizing large noisy multiparty quantum states using genuine multiparty
entanglement is a challenging task. In this paper, we calculate lower bounds of
genuine multiparty entanglement localized over a chosen multiparty subsystem of
multi-qubit stabilizer states in the noiseless and noisy scenario. In the
absence of noise, adopting a graph-based technique, we perform the calculation
for arbitrary graph states as representatives of the stabilizer states, and
show that the graph operations required for the calculation has a polynomial
scaling with the system size. As demonstrations, we compute the localized
genuine multiparty entanglement over subsystems of large graphs having linear,
ladder, and square structures. We also extend the calculation for graph states
subjected to single-qubit Markovian or non-Markovian Pauli noise on all qubits,
and demonstrate, for a specific lower bound of the localizable genuine
multiparty entanglement corresponding to a specific Pauli measurement setup,
the existence of a critical noise strength beyond which all of the post
measured states are biseparable. The calculation is also useful for arbitrary
large stabilizer states under noise due to the local unitary connection between
stabilizer states and graph states. We demonstrate this by considering a toric
code defined on a square lattice, and computing a lower bound of localizable
genuine multiparty entanglement over a non-trivial loop of the code. Similar to
the graph states, we show the existence of the critical noise strength in this
case also, and discuss its interesting features.
