Measurement of GHZ and cluster state entanglement monotones in transmon
  qubits
Experimental detection of entanglement in superconducting qubits has been
mostly limited, for more than two qubits, to witness-based and related
approaches that can certify the presence of some entanglement, but not
rigorously quantify how much. Here we measure the entanglement of three- and
four-qubit GHZ and linear cluster states prepared on the 16-qubit IBM
Rueschlikon (ibmqx5) chip, by estimating their entanglement monotones. GHZ and
cluster states not only have wide application in quantum computing, but also
have the convenient property of having similar state preparation circuits and
fidelities, allowing for a meaningful comparison of their degree of
entanglement. We also measure the decay of the monotones with time, and find in
the GHZ case that they actually oscillate, which we interpret as a drift in the
relative phase between the $|0\rangle^{\otimes n}$ and $|1\rangle^{\otimes n}$
components, but not an oscillation in the actual entanglement. After
experimentally correcting for this drift with virtual Z rotations we find that
the GHZ states appear to be considerably more robust than cluster states,
exhibiting higher fidelity and entanglement at later times. Our results
contribute to the quantification and understanding of the strength and
robustness of multi-qubit entanglement in the noisy environment of a
superconducting quantum computer.
Amara Katabarwa Michael R. Geller