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Entanglement is a central concept in quantum information and a key resourcefor many quantum protocols. In this work we propose and analyze a class ofentanglement witnesses that detect the presence of entanglement in subsystemsof experimental multi-qubit stabilizer states. The witnesses we propose can bedecomposed into sums of Pauli operators and can be efficiently evaluated byeither two measurement settings only or at most a number of measurements thatonly depends on the size of the subsystem of interest. We provide twoconstructive methods to design the local witness operators, the first one basedon the local unitary equivalence between graph and stabilizer states, and thesecond one based on sufficient and necessary conditions that the respective setof constituent Pauli operators needs to fulfill. We theoretically establish thenoise tolerance of the proposed witnesses and benchmark their practicalperformance by analyzing the local entanglement structure of an experimentalseven-qubit quantum error correction code.

Design and Experimental Performance of Local Entanglement Witness Operators