Demonstration of tripartite cat states in two distinct classes of entanglement

arXiv:2607.12317 · quant-ph · Submitted 2026-07-14 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Hi, I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Demonstration of tripartite cat states in two distinct classes of entanglement".

Mira: Here's the gist of the paper. The gist: This work experimentally realizes macroscopic tripartite entangled cat states of two distinct classes, GHZ-cat and W-cat states, encoded across three microwave resonators coupled to an ancillary superconducting transmon.

Kai: Entanglement Classes and Properties The paper demonstrates the experimental synthesis and characterization of two distinct classes of tripartite macroscopic entanglement, specifically the GHZcat⟩ state and the Wcat⟩ state, in three quantum harmonic oscillators hosted in a bosonic circuit quantum electrodynamics (cQED) hardware <ref:2607.12317#pg3>.

Mira: These states are fundamentally inequivalent, with GHZ-type states lacking pairwise entanglement and W-type states retaining residual bipartite entanglement <ref:2607.12317#pg5>.

Kai: The GHZ-cat state is defined as GHZcat⟩ ∝ α, α, α⟩ + -α,-α,-α⟩ <ref:2607.12317#pg6>, while the W-cat state is defined as Wcat⟩ ∝ α, -α, -α⟩ + -α, α, -α + -α, -α, α <ref:2607.12317#pg6>.

Title and authors: Kai: The paper we're looking at is titled "Demonstration of tripartite cat states in two distinct classes of entanglement." It’s about showing that we can experimentally create two fundamentally different types of macroscopic entangled cat states using three resonators linked to a transmon.

Mira: And the authors are Chee Loke, Jonathan Schwinger, Kehui Yu, Yingshan Zhang, Amon M. Kasper, Tanjung Krisnanda and Yvonne Y. Gao. They are showing that while bipartite entanglement is common, genuine multipartite entanglement is harder to access in the continuousvariable domain.

Lev: So what's the simple translation of this title? It means they managed to build two distinct types of genuine multipartite entanglement—the GHZ-cat and W-cat states—and they showed how to make them using a specific hardware setup.

Kai: Exactly. The authors are demonstrating that these two classes have different properties, which is important for understanding how complex quantum correlations work in larger systems.

Mira: It sets up the context for why we need to know the difference between GHZ and W entanglement, because they are not equivalent states in any useful way.

Lev: So we're moving past just studying simple two-mode entanglement and into demonstrating genuine multipartite behavior across three modes using this setup.

Kai: It’s about proving that even in a continuousvariable system, we can engineer these specific complex structures by utilizing the transmon's energy levels for conditional operations.

Mira: And the authors are laying out the whole experimental architecture right there, showing how they put Alice, Bob and Charlie resonators relative to each other and the central chip.

The paper's summary: Kai: To summarize, this paper experimentally realizes macroscopic tripartite entangled cat states of two distinct classes, the GHZ-cat and W-cat states. These are encoded across three microwave resonators coupled to an ancillary superconducting transmon.

Mira: The core idea is that they developed one-to-all conditional controls on those three oscillators by fully utilizing the three energy levels of the transmon to generate these states in a single piece of hardware.

Lev: So, it’s not just one gate; it’s a whole sequence of operations, which means we need to be careful about how robust that sequence is when we try to use it for something else.

Kai: They used specific sequences like transmon rotation, an ECD gate, another transmon rotation and then some post-selection to prepare the GHZ-cat state. For the W-cat state preparation involved distributing its three components onto the transmon levels g, e, and f and then collecting them onto level g.

Mira: And that W-cat sequence used an uneven echoed conditional displacement gate to implement conditional displacement within the g–f subspace while leaving the e component undisturbed.

Lev: So they're not just doing a simple state preparation; they’s performing some specific, tailored operations on different subspaces of the system.

Kai: It’s about showing that you can use this hardware to generate these distinct structures, which is a big step for realizing complex quantum states in real labs.

The paper's improvements: Mira: What's interesting about what they suggest is how they’re using the results to demonstrate the clear difference between pairwise entanglement and genuine multipartite entanglement.

Kai: They show that by measuring specific three-mode correlations like XXX, XY Y, Y XY, and Y Y X, you can reveal a clear violation of Mermin’s inequality with Ms equal to two point four eight plus or minus zero point nine for the GHZ-cat state.

Lev: So that Mermin’s inequality violation is the real gold standard here because it proves they're actually got something non-local and non-classical happening across all three modes simultaneously.

Mira: For the W-cat state, you get nonzero two-mode correlations like XXI, Y Y I, and XIX which represent coherences corresponding to pairwise entanglement.

Lev: That’s what we need to know; that distinction is what allows us to separate states that might look similar but have different physical implications for things like quantum error correction.

Kai: The paper also shows the fidelity of zero point eighty-three plus or minus zero point two and zero point seventy plus or minus zero point two which both pass the thresholds for genuine multipartite entanglement.

Mira: So they're not just getting high numbers; they are hitting the required benchmarks for what we’re trying to achieve in these continuousvariable bosonic codes.

Lev: The paper also points out that with improved lifetimes, those fidelities could reach zero point ninety-three plus or minus zero point three and zero point eighty-eight plus or minus zero point three.

Conclusion: Kai: So, in summary of the paper "Demonstration of tripartite cat states in two distinct classes of entanglement," they experimentally realized two distinct classes: GHZ-cat and W-cat states using three resonators coupled to a transmon.

Mira: The key points are that the GHZ-cat state shows no bipartite entanglement, while the W-cat state retains about sixty-four point of its ideal entanglement after tracing out one mode.

Lev: It’s about having a measurable signature for genuine multipartite correlation in both cases, which is what we need to know for practical applications.

Kai: The implication is that this work provides a valuable testbed for future studies of macroscopic many-body entanglement and fault-tolerant quantum information processing with multipartite bosonic codes.

Mira: It offers a way to generate distinct classes of CV entangled states and characterize their properties without needing computationally expensive full-space tomography.

Lev: It's a promising building block for potential multimode quantum error-correction architectures, provided we can solve those loss problems they highlighted.

Centre for Quantum Technologies, National University of Singapore · Department of Physics, National University of Singapore

quant-ph

Submitted: 2026-07-14

Updated: 2026-10-21

Comments: Main text: 7 pages, 4 figures. Appendix: 18 pages, 9 figures

Code: https://github.com/tkrisnanda/GHZ_W_cat

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 90/100

The gist: The gist: This work experimentally realizes macroscopic tripartite entangled cat states of two distinct classes, GHZ-cat and W-cat states, encoded across three microwave resonators coupled to an

Key concepts

GHZ-cat state: This is a specific type of three-mode entangled cat state defined by two components, |α, α, α⟩ and |-α,-α,-α⟩. A key feature is that this state lacks any pairwise entanglement between the individual modes. It serves as a benchmark for multipartite entanglement studies.
W-cat state: This is another distinct tripartite entangled cat state defined by three components: |α, -α, -α⟩ + |-α, α, -α| + |-α, -α, α|. Unlike the GHZ-cat state, the W-cat state retains residual bipartite entanglement even after tracing out one mode. This makes it important for studying entanglement robustness.
cQED hardware: This refers to a quantum electrodynamics setup where microwave resonators (the oscillators) are coupled to a central superconducting transmon. This architecture allows for precise control over the three modes by using the transmon's energy levels to perform complex, one-to-all unitary operations in a single physical device.
Subspace Tomography: This is an efficient mathematical method used to reconstruct the quantum state of a system. Instead of measuring every possible state, this technique maps expectation values of Pauli operators onto characteristic function points. It allows researchers to accurately verify the GHZ-cat and W-cat states with high fidelity (0.83 and 0.70, respectively).

Terminology

Entanglement — 8× in this paper · explained in 4 episodes
Multipartite Entanglement — 1× in this paper · explained in 3 episodes

Summary

The gist: This work experimentally realizes macroscopic tripartite entangled cat states of two distinct classes, GHZ-cat and W-cat states, encoded across three microwave resonators coupled to an ancillary superconducting transmon.

Entanglement Classes and Properties

The paper demonstrates the experimental synthesis and characterization of two distinct classes of tripartite macroscopic entanglement, specifically the GHZcat⟩ state and the Wcat⟩ state, in three quantum harmonic oscillators hosted in a bosonic circuit quantum electrodynamics (cQED) hardware <ref:2607.12317#pg3>. These states are fundamentally inequivalent, with GHZ-type states lacking pairwise entanglement and W-type states retaining residual bipartite entanglement <ref:2607.12317#pg5>. The GHZ-cat state is defined as GHZcat⟩ ∝ α, α, α⟩ + -α,-α,-α⟩ <ref:2607.12317#pg6>, while the W-cat state is defined as Wcat⟩ ∝ α, -α, -α⟩ + -α, α, -α + -α, -α, α <ref:2607.12317#pg6>. The GHZ-cat state exhibits no bipartite entanglement while the W-cat state retains 64% of its ideal entanglement after a partial trace over one of the modes <ref:2607.12317#pg5>.

Hardware and Control Architecture

The realization is achieved using a bosonic cQED architecture where three oscillators, Alice (red), Bob (turquoise), and Charlie (yellow), are arranged perpendicularly above and below a central chip hosting an ancillary transmon <ref:2607.12317#pg3>. The hardware enables one-to-all controlled unitary operations over the three oscillators by fully utilizing three energy levels of the transmon to generate these states in a single piece of hardware <ref:2607.12317#pg2>. This is accomplished by engineering one-to-all controlled unitary operations and employing an efficient subspace tomography protocol for state reconstruction <ref:2607.12317#pg2>. The interaction between the transmon and the three oscillators is governed by a dispersive coupling Hamiltonian <ref:2607.12317#pg5>.

State Preparation Protocols

The GHZ-cat state is prepared with a sequence involving a transmon rotation, an ECD gate, another transmon rotation, and a post-selection <ref:2607.12317#pg5>. The W-cat state preparation involves distributing its three components onto the transmon levels g⟩, e⟩, and f⟩ and then collecting them onto g⟩ <ref:2607.12317#pg5>. The W-cat sequence utilizes an Uneven Echoed Conditional Displacement (UECD) gate to implement conditional displacement within the g–f subspace while leaving the e⟩ component undisturbed <ref:2607.12317#pg7>.

Characterization and Verification

The characterization relies on an efficient three-mode tomography technique based on mapping the expectation value of Pauli operators to joint three-mode characteristic function points <ref:2607.12317#pg6>. For the GHZ-cat state, it is shown that nonzero values for the three-mode correlations XXX, XY Y, Y XY, and Y Y X reveal a clear violation of Mermin’s inequality with Ms = 2.48 ± 0.09 <ref:2607.12317#pg6>. For the W-cat state, nonzero two-mode correlations like XXI, Y Y I, and XIX represent coherences corresponding to pairwise entanglement <ref:2607.12317#pg5>. The fidelity of the GHZ-cat state is reported as 0.83 ± 0.02 and the W-cat state as 0.70 ± 0.02, both exceeding their respective thresholds for genuine multipartite entanglement <ref:2607.12317#pg2>.

Error Analysis and Limitations

The error analysis details the contribution of transmon energy decay, pure dephasing, and oscillator photon loss during both state preparation and characterization <ref:2607.12317#pg9>. The oscillators’ photon loss is identified as the major detrimental factor for the two- and three-mode correlations in both states <ref:2607.12317#pg9>. The paper shows that for the GHZ-cat state, the detrimental factors due to oscillators’ photon loss are ˜f1 ≈ 0.90 <ref:2607.12317#pg9>. For the W-cat state, these factors are denoted as ˜f1(AB), ˜f1(AC), and ˜f1(BC) with values approximately equal to 0.92, 0.95, and 0.92 respectively <ref:2607.12317#pg9>. The primary factors limiting the fidelities are the relatively short oscillator coherence times of 50 − 100 µs <ref:2607.12317#pg10>.

Future Directions

The results provide a valuable testbed for future studies of macroscopic many-body entanglement and fault-tolerant quantum information processing with multipartite bosonic codes <ref:2607.12317#pg6>. The technique offers an effective tool for generating distinct classes of tripartite CV entangled states and characterizing their properties <ref:2607.12317#pg5>. This work also provides new ingredients for versatile multi-oscillator control and a promising building block for potential multimode quantum error-correction architectures <ref:2607.12317#pg10>. The analysis suggests that with improved lifetimes, fidelities could reach 0.93±0.03 and 0.88±0.03 for the GHZ-cat and W-cat states respectively <ref:2607.12317#pg10>.

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Improvements for AI systems

Enables on-demand generation of two distinct classes of macroscopic tripartite entangled cat states, GHZ-cat and W-cat states, using a single piece of hardware by utilizing three microwave resonators coupled to an ancillary superconducting transmon. This allows for the experimental realization and characterization of genuine multipartite entanglement in the continuousvariable regime.
Allows for one-to-all conditional controls on the three oscillators by fully utilizing three energy levels of the transmon, enabling efficient state generation in a single hardware setup. This capability is essential for building scalable quantum systems requiring precise control over many interacting modes.
Implements an efficient subspace tomography protocol that reconstructs GHZ-cat and W-cat states with high fidelity (0.83 ± 0.02 and 0.70 ± 0.02, respectively). This allows AI systems to accurately measure and verify genuine multipartite entanglement in continuousvariable bosonic codes without requiring computationally prohibitive full-space tomography.
Provides a method for validating the distinct entanglement classes by experimentally demonstrating that pairwise entanglement is present in the W-cat state but absent in the GHZ-cat state. This capability allows AI to distinguish between different types of quantum correlations and their physical implications for applications like quantum error correction.
Offers a valuable testbed for future studies of macroscopic many-body entanglement and fault-tolerant quantum information processing with multipartite bosonic codes. This enables AI research into the fundamental structure of entanglement, its robustness against loss, and practical witnesses capable of detecting non-Gaussian entanglement.
Enables the development of versatile multi-oscillator control protocols by providing joint ECD and UECD operations on three oscillators. This provides new ingredients for scalable control in future quantum architectures beyond existing two-mode Bell-cat demonstrations.

Abstract

Entanglement is a cornerstone of quantum mechanics and an essential resource for quantum computation, communication, and metrology. While bipartite entanglement is extensively studied, genuine multipartite entangled states remain largely inaccessible in the continuous-variable domain. Here, we experimentally realize continuous-variable tripartite entangled cat states of the two distinct classes with fundamentally inequivalent properties, namely GHZ-cat and W-cat states, encoded across three microwave resonators coupled to an ancillary superconducting transmon. We develop one-to-all conditional controls on the three oscillators by fully utilizing three energy levels of the transmon to generate these states in a single piece of hardware and employ an efficient subspace tomography protocol for state reconstruction. We obtain measurement-corrected state fidelities of 0.83 plus or minus0.02 for GHZ-cat and 0.70 plus or minus0.02 for W-cat, both exceeding the thresholds for genuine multipartite entanglement, with the W-state certification further supported by an optimized fully decomposable witness directly computed with the reconstructed density matrix. We validate the distinct entanglement classes by experimentally demonstrating that pairwise entanglement is present in the W-cat state but absent in the GHZ-cat state. Our technique for the on-demand generation and characterization of inequivalent classes of tripartite continuous-variable entanglement provides a testbed for studying multipartite bosonic entanglement and its robustness to loss, and a building block for future quantum information processing with multipartite bosonic codes.