Efficient entanglement generation and detection of generalized stabilizer states

The generation and verification of large-scale entanglement are essential to the development of quantum technologies. In this paper, we present an efficient scheme to generate genuine multipartite entanglement of a large number of qubits by using the Heisenberg interaction. This method can be conveniently implemented in various physical platforms, including superconducting, trapped-ion, and cold-atom systems. In order to characterize the entanglement of the output quantum state, we generalize the stabilizer formalism and develop an entanglement witness method. In particular, we design a generic searching algorithm to optimize entanglement witness with a minimal number of measurement settings under a given noise level. From the perspective of practical applications, we numerically study the trade-off between the experiment efficiency and the detection robustness.

Figure 1

Genuine multipartite entangled target state. The qubit pairs connected by solid lines denote singlets, and the dashed ovals are $\sqrt{\mathrm{SWAP}}$ gates.

Figure 2

Optimal EWs obtained by the numerical searching algorithm for $N=8,10,15,20$ entangled states. The minimum requirements for the experimental fidelity under different cases are plotted versus LMC. Note that $F_{\min }$ decreases more and more slowly when LMC increases and finally reaches the lower bound $1-p_{max}$ [see Eq. (20)], which approaches 81.25% when $N$ is large.