Measurement of GHZ and cluster state entanglement monotones in transmon qubits

TL;DR

This paper experimentally measures and compares the entanglement monotones of three- and four-qubit GHZ and cluster states on a superconducting quantum chip, revealing their robustness and decay behaviors in noisy conditions.

Contribution

First direct measurement of multi-qubit entanglement monotones in superconducting qubits, providing insights into their robustness and decay over time.

Findings

GHZ states show oscillating entanglement monotones due to phase drift.

GHZ states are more robust than cluster states in noisy environments.

Entanglement monotones decay over time but can be corrected for phase drift.

Abstract

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.