Improving the Rate-Loss Scaling in Polarization Entanglement Distribution using Single-Click Entanglement Swapping

arXiv:2507.14836 · quant-ph · Submitted 2025-07-20 · Read on arXiv

Listen

Radio episode about this paper

Transcript

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

Kai: Today's paper: "Improving the Rate-Loss Scaling in Polarization Entanglement Distribution using Single-Click Entanglement Swapping".

Mira: The gist The authors experimentally demonstrate that they can overcome the conventional rate-loss scaling limit of O(ηC) for distributing polarization entangled photon pairs by integrating single-click entanglement swapping and hybrid…

Kai: First, who's behind it and why it matters.

Paper summary: Kai: We just looked at how this paper tackles that linear rate loss scaling O(ηC) for polarization entanglement distribution and it seems they solve it by combining two things: single-click entanglement swapping and hybrid entanglement between polarization and photon-number qubits >

Mira: That’s right, the thesis is that these specific techniques allow them to overcome the conventional rate-loss scaling limit, achieving a square root improvement in that scaling >

Lev: So if you take the naive question a listener might ask about this paper, it's how exactly do they manage to get that entanglement swapping working when one of the modes is described by a single photon state >

Kai: Well, they use the superposition of vacuum and single-photon states in their single-click swapping mechanism which leverages that superposition to surpass direct transmission scaling >

Mira: And for generating this hybrid entanglement, they combine a two-mode polarization squeezed vacuum with vertically polarized weak coherent light using a polarizing beam splitter to mix them >

Lev: That mixing process leads to the hybrid state at Alice's side being described as ψ⟩AC1 = α V⟩A zero⟩C1 + γ H⟩A one⟩C1 > <ref:2507.14836#pg2,as |ψ⟩AC1 = α |V⟩A |0⟩C1 + γ |H⟩A |1>

Kai: And they prepare the same hybrid entanglement at Bob's side, denoted as ψ⟩BC2, and then send those modes C1 and C2 through channels with transmittance √ηC to the swapping node >

Mira: The success of the swapping happens when a single-photon detection occurs at one of the output ports of that BS, which projects onto Ψ+01C1C2 = (⟨0C1 ⟨1C2 + ⟨1C1 ⟨0C2) / √two > <ref:2507.14836#pg2>

Lev: That successful projection gives them the final polarization entangled state in A and B, which is Ψ+pol⟩AB = one/√two (H⟩A V⟩B + V⟩A H⟩B) > <ref:2507.14836#pg1>

Kai: The numbers they present are that the ideal success probability scales with √ηC for channel transmission while the rate of directly transmitting polarization entangled photons from Alice to Bob is proportional to ηC >

Mira: They also mention that the factor α 2γ squared in their success probability reflects that the generated polarized photon pair consists of one photon from the TMSV and another photon from the coherent state > <ref:2507.14836#pg1>

Lev: The caveat they bring up is that unwanted optical losses are estimated using ηLC = ηD = one point zero, which they show as a red dotted line in Figure five > <ref:2507.14836#pg1>

Kai: So basically, this paper shows a protocol of efficiently distributing polarization entanglement by using hybrid entanglement sources and single-click entanglement swapping >

Mira: It really highlights the square root advantage of the rate-loss scaling when compared to standard entanglement swapping protocols >

Conclusion: Kai: So wrapping up "Improving the Rate-Loss Scaling in Polarization Entanglement Distribution using Single-Click Entanglement Swapping" by Hikaru Shimizu and his team, it seems they’ve really shown a practical way to improve the rate of distributing polarization entanglement >

Mira: They did prove that using hybrid entanglement sources and single-click swapping leads to a distributed state with high fidelity, experimentally observed at zero point eight four three plus or minus zero point zero seven four >

Lev: I think what this means for the field is that they’ve shown a way to make these systems more efficient without having to rely on perfect channel conditions >

Kai: The title of the paper points right to the core idea: improving the rate-loss scaling, and it shows they did that by showing how this is done using single-click entanglement swapping >

Mira: It really accelerates research into large-scale quantum network applications because this technique is directly applicable to protocols for efficiently distributing multipartite polarization entangled states >

Lev: So the final word is that we now have a method that can push the scaling limits of these distribution protocols by demonstrating a square root improvement over what was previously achievable >

Department of Electronics and Electrical Engineering, Keio University · School of Fundamental Science and Technology, Keio University · Center for Spintronics Research Network, Keio University · Graduate School of Engineering Science, Osaka University · Center for Quantum Information and Quantum Biology, Osaka University · National Institute of Information and Communications Technology (NICT)

quant-ph

Submitted: 2025-07-20

Updated: 2025-08-09

Comments: 12 pages, 9 figures

Journal ref: Optica 13, 1838-1844 (2026)

DOI: 10.1364/OPTICA.590840

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 91/100

The gist: The gist The authors experimentally demonstrate that they can overcome the conventional rate-loss scaling limit of O(ηC) for distributing polarization entangled photon pairs by integrating

Key concepts

Single-Click Entanglement Swapping
This technique uses the superposition of vacuum and single-photon states to perform entanglement swapping in a way that surpasses direct transmission scaling limitations. It leverages the properties of these specific quantum states to enhance the efficiency of distributing entanglement over lossy channels.
Hybrid Entanglement
This involves combining two different types of quantum states: a two-mode polarization squeezed vacuum and vertically polarized weak coherent light. These are mixed using a polarizing beam splitter to create an entangled state that links polarization information with photon-number information, which is crucial for the protocol's performance.
Rate-Loss Scaling
This refers to how the achievable rate of distributing entanglement decreases as the transmission loss in optical channels increases. Conventional methods suffer from a linear scaling limit (O(ηC)), but this new method achieves a square root improvement, meaning it maintains better performance even in lossy environments.
Bell Test (CHSH)
This is an experimental test used to verify if the distributed polarization-entangled photons exhibit genuine quantum correlations. The observed S parameter value of 2.302 strongly violates the local hidden variable theory's upper bound, confirming that the entanglement is truly non-classical and useful for quantum communication.

Terminology

Summary

The gist The authors experimentally demonstrate that they can overcome the conventional rate-loss scaling limit of O(ηC) for distributing polarization entangled photon pairs by integrating single-click entanglement swapping and hybrid entanglement between polarization and photon-number qubits, achieving a square root improvement in this scaling.

Protocol Overview

The protocol combines two key ideas to improve the rate-loss scaling:

  1. Single-click entanglement swapping, which utilizes the superposition of the vacuum and single-photon states, known to surpass direct transmission scaling.

  2. Hybrid entanglement between polarization and photon-number qubits, obtained by generating normal polarization or photon-number qubit entanglement and converting the degree of freedom of one of the modes.

The basic idea involves preparing hybrid entanglement sources at two end-users, Alice and Bob, sending the photon-number superposition parts to lossy channels for swapping, leveraging improved scaling via single-click swapping, and resulting in a polarization entangled photon pair shared by Alice and Bob.

Hybrid Entanglement Generation

The hybrid entanglement is generated by combining two optical quantum states:

  1. The two-mode polarization squeezed vacuum (TMSV) described as TMSV⟩ ∼ 0H0V ⟩ + γ 1H1V ⟩ + O(γ2), where 0H(V) is a vacuum state and 1H(V) is a single-photon state in the H(V)-polarized mode.

  2. Vertically polarized weak coherent light described as α⟩ ∼ 0V ⟩ + α 1V ⟩ + O(α2), where α≪1.

These states are mixed by using a polarizing beam splitter (PBS). At Alice’s side, post-selecting events where one or more photons exist in mode A yields an unnormalized hybrid state ψ⟩AC1= α V ⟩A 0⟩C1 + γ H⟩A 1⟩C1. The same hybrid entanglement is prepared at Bob’s side, denoted as ψ⟩BC2.

Entanglement Swapping and Rate-Loss Scaling

The states in modes C1 and C2 are sent to the swapping node through optical channels with transmittance √ηC. Successful swapping occurs if single-photon detection happens at one of the output ports of the BS in the swapping node, projecting onto Ψ+01C1C2= (⟨0C1 ⟨1C2 + ⟨1C1 ⟨0C2) / √2. The resulting unnormalized state in A and B is given as Ψ+pol⟩AB = 1/√2 (H⟩A V⟩B + V⟩A H⟩B).

The ideal success probability of the protocol scales with √ηC for channel transmission while the rate of directly transmitting polarization entangled photons from Alice to Bob is proportional to ηC. The factor α2γ2 in the success probability reflects that the generated polarized photon pair consists of one photon from the TMSV and another photon from the coherent state. Unwanted optical losses are estimated using ηLC = ηD = 1.0, shown as a red dotted line in Fig. 5.

Fidelity and Performance

The fidelity to the ideal polarization entangled state is experimentally found to be 0.843 ± 0.074. The theoretical model including mode mismatches estimates the fidelity as (1 + MAMB)/2 = 0.907 ± 0.003, which fits with the experimental result. The distribution rate of our protocol is estimated by Rhybrid = α2/γ2√ηC × η2/LC × η3D × frep. This result outperforms standard entanglement swapping and shows the square-root advantage of the rate-loss scaling.

Bell Test

A CHSH-type Bell test was performed on the distributed polarization-entangled photons, yielding an observed S parameter of 2.302 ± 0.066, which is in good agreement with the simulation result of 2.313. The experimental value clearly violates the upper bound of 2 predicted by any local hidden variable theory by approximately 5 standard deviations.

Multipartite Entanglement Distribution

The study is compatible with a loss-tolerant protocol of multi-partite entanglement distribution proposed in Refs. [1, 2]. In this protocol, the distribution rate of direct transmission scales as ηC. In the hybrid approach, the distribution rate depends on the success probability of getting the target detection pattern and detection probability in all user nodes. The GHZ-state distribution rate is proportional to α4γ4 × η1/2C × frep. The advantage of the hybrid approach for the GHZ-state distribution is its robustness against noise arising from multiple photon detection at the central node.

Conclusion

The authors demonstrate a protocol of efficiently distributing polarization entanglement by using hybrid entanglement sources and single-click entanglement swapping The distributed state shows high fidelity to the ideal polarization Bell state and experimentally observes the square-root improvement of the rate-loss scaling from conventional protocols. In addition, their technique is directly applicable to the protocol of efficiently distributing multipartite polarization entangled states. The study accelerates research into large-scale quantum network applications.

Acknowledgements

R.I. and M.T. acknowledge the members of the Quantum Internet Task Force for comprehensive and interdisciplinary discussions on the quantum internet. This work was supported by JST CREST, JPMJCR24A5; MEXT Q-LEAP, JPMXS0118067395; Center for Spintronics Research Network (CSRN), Keio University; NEXT Leading Initiative for Excellent Young Researchers; Program for the Advancement of Next Generation Research Projects, Keio University; JST CRONOS, JPMJCS24N6; JST ASPIRE, JPMJAP2427; JST Moonshot R&D, JPMJMS2061, JPMJMS226C, and FOREST Program.

References

[1] A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, Nonmaximally Entangled States: Production, Characterization, and Utilization

[2] D. F. V. James, P. G., W., J., M., A.-G., Measurement of qubits

[3] M. Giustina, M. A., S., J.-H., A.-H., K.-Phelan, F. Steinlechner, J. Kofler, J. Larsson, C.-Abell´an, W. Amaya, V. Pruneri

[4] Y. Tsujimoto, K., Wakui, M., Fujiwara, K., Hayasaka, S., Miki, H., Terai, M., Sasaki, and M. Takeoka

[5] W.-Z. Liu, Y.-Z. Zhang, Y.-Z. Zhen, M.-H. Li, Y. Liu, J. Fan, FXu, QZhang, and J.

Improvements for AI systems

  1. Improve quantum network routing algorithms by incorporating square root improvement of the rate-loss scaling from conventional approaches into network topology optimization models, potentially allowing for more efficient path selection through lossy channels.

  2. Develop a new class of quantum communication protocols capable of achieving a fidelity of 0.843 for the distributed polarization entangled photon pairs, enabling higher-quality entanglement distribution over long-haul optical links compared to existing methods scaling at O(ηC).

  3. Design more robust quantum repeater node architectures by leveraging the concept that this improvement is equivalent to that achieved by 1-hop quantum repeater node, potentially simplifying the physical implementation requirements for near-future quantum network components.

  4. Engineer AI systems for multipartite entanglement distribution (GHZ and W states) by implementing a protocol where the advantage compared to the direct transmission is more prominent than that of the bipartite case [46], thereby reducing the multi-photon effects observed in Ref. [33] by the entanglement distillation-like effect.

  5. Create machine learning models for optimizing resource allocation in quantum networks, specifically training them on the distribution rate of our protocol Rhybrid is estimated to be Rhybrid = α2/2√ηC × η2/LC × η3D × frep to maximize network throughput under realistic loss conditions.

Sources

Related papers