Demonstration of tripartite cat states in two distinct classes of entanglement

This study investigates the experimental generation and characterization of multipartite entanglement in macroscopic continuous-variable (CV) systems. Specifically, the authors aim to synthesize two fundamentally inequivalent classes of tripartite entangled states—GHZ-cat and W-cat states—within a bosonic circuit quantum electrodynamics (cQED) architecture.

The researchers utilize a hardware platform consisting of three superconducting hairpin resonators coupled to a single ancillary transmon. By leveraging the transmon's three energy levels, they implement one-to-all conditional control operations. This is achieved through an extension of the Echoed Conditional Displacement (ECD) gate, which allows for precise manipulation of the oscillators without requiring perfectly matched coupling strengths. To verify the entanglement, the team employs an efficient subspace tomography protocol, which reconstructs the state by measuring only a subset of the joint characteristic function, significantly reducing the experimental complexity compared to full-space tomography.

The experimental team successfully prepared GHZ-cat and W-cat states with fidelities of 0.83 and 0.70, respectively. These values exceed the thresholds required to certify genuine multipartite entanglement. Furthermore, the authors validated the distinct nature of these entanglement classes by demonstrating that the W-cat state retains pairwise entanglement after a partial trace, whereas the GHZ-cat state does not. The non-local nature of the GHZ-cat state was further confirmed through the violation of Mermin's inequality.

This work provides a scalable testbed for exploring macroscopic many-body entanglement and quantum information processing. By demonstrating the ability to generate and distinguish between inequivalent classes of tripartite entanglement in a bosonic system, the study offers a foundation for future research into fault-tolerant quantum error correction and the fundamental physics of the quantum-to-classical transition.