Design and experimental performance of local entanglement witness operators

Entanglement is a central concept in quantum information and a key resource for many quantum protocols. In this work we propose and analyze a class of entanglement witnesses that detect the presence of entanglement in subsystems of experimental multi-qubit stabilizer states. The witnesses we propose can be decomposed into sums of Pauli operators and can be efficiently evaluated by either two measurement settings only or at most a number of measurements that only depends on the size of the subsystem of interest. We provide two constructive methods to design the local witness operators, the first one based on the local unitary equivalence between graph and stabilizer states, and the second one based on sufficient and necessary conditions that the respective set of constituent Pauli operators needs to fulfill. We theoretically establish the noise tolerance of the proposed witnesses and benchmark their practical performance by analyzing the local entanglement structure of an experimental seven-qubit quantum error correction code