arxiv: 2604.17196 · v1 · submitted 2026-04-19 · 🪐 quant-ph

Recognition: unknown

Coherence Transfer in Quantum Networks

Chun-Yang Lin , Yu-Cheng Li , Shih-Hsuan Chen , Sheng-Yan Sun , Ching-Jui Huang , Kuan-Jou Wang , Che-Ming Li

Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:43 UTC · model grok-4.3

classification 🪐 quant-ph

keywords coherence transferquantum networksnonlinear criterionentanglement networksmulti-photon entanglementquantum information

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The pith

A nonlinear criterion identifies coherence transfer in quantum networks using only two measurements regardless of size or node characterization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a practical way to detect when coherence is transferred through quantum networks. It combines static and dynamic features of coherence into a nonlinear test that needs just two population measurements in an experimental basis. This approach works even if some nodes have unknown verification abilities and applies to networks of any size. Such a tool matters because full characterization is often impossible in real experiments, yet confirming coherence transfer is essential for quantum communication and information processing.

Core claim

We use static and dynamic coherence features to introduce a nonlinear criterion for identifying coherence transfer. The criterion requires only two measurement settings for network-state populations in an experimental state basis, regardless of the network's size. It remains valid even when the verification capabilities of checkpoint nodes are uncharacterized. The principle and method are general, encompassing networks with different access levels and scenarios, from those requiring no input changes to those involving coherence dynamics in the time domain.

What carries the argument

The nonlinear criterion based on static and dynamic coherence features that detects transfer via two population measurements in an experimental state basis.

If this is right

Enables coherence transfer detection in networks of arbitrary size using a fixed number of measurements.
Applies across scenarios including static cases with no input changes and dynamic cases in the time domain.
Provides experimental evidence of coherence transfer in four- and six-photon entanglement networks via remote state preparation and entanglement swapping.
Remains effective for networks with varying access levels and uncharacterized checkpoint nodes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This approach could reduce the experimental overhead needed to verify resources in large-scale quantum networks.
The criterion might be adapted to detect transfer of other quantum features like entanglement in partially known systems.
Further experiments could test its performance in continuous-variable or solid-state quantum platforms.

Load-bearing premise

The nonlinear criterion remains valid even when the verification capabilities of checkpoint nodes are uncharacterized, allowing detection without full system knowledge.

What would settle it

An experiment in which coherence is transferred but the two-measurement nonlinear criterion fails to detect it, or falsely detects transfer when none occurs.

Figures

Figures reproduced from arXiv: 2604.17196 by Che-Ming Li, Ching-Jui Huang, Chun-Yang Lin, Kuan-Jou Wang, Sheng-Yan Sun, Shih-Hsuan Chen, Yu-Cheng Li.

**Figure 1.** Figure 1: FIG. 1. Coherence transfer in quantum networks and its detection. The coherence transfer criterion (1) and its temporal [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Detecting coherence transfer in single-electron trans [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Detection of experimental coherence transfer in multi-photon entanglement networks. (a) Experimental setup. The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Experimental one-qubit coherence transfer. Schemes: [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

read the original abstract

Detecting coherence transfer in complex quantum networks can be challenging due to uncharacterized experimental conditions and limited system access. Here, we use static and dynamic coherence features to introduce a nonlinear criterion for identifying coherence transfer. The criterion requires only two measurement settings for network-state populations in an experimental state basis, regardless of the network's size. It remains valid even when the verification capabilities of checkpoint nodes are uncharacterized. The principle and method are general, encompassing networks with different access levels and scenarios, from those requiring no input changes to those involving coherence dynamics in the time domain. Experimentally, using remote state preparation and entanglement swapping, we transfer single polarization qubits and polarization-entangled pairs in four- and six-photon entanglement networks. The criterion provides experimental evidence of coherence transfer in multi-photon entanglement networks. Our findings offer a practical tool for coherence transfer in quantum information and open quantum systems in networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a nonlinear criterion for spotting coherence transfer from two population measurements that holds even with uncharacterized checkpoint nodes, but the supporting derivation leaves room for mimicry by unknown node operations.

read the letter

The main takeaway is that this work offers a low-overhead way to check coherence transfer in quantum networks without needing to characterize every node or run many measurements. They combine static and dynamic coherence features into a nonlinear test that uses only two settings on the network-state populations in the experimental basis, and they show it applies across different access levels, including time-domain dynamics. The experiments with remote state preparation and entanglement swapping in four- and six-photon setups provide concrete evidence that the criterion flags transfer in real multi-photon entanglement networks. That minimalism and the experimental demonstration are the parts that stand out as useful for people working on scalable verification or open-system studies in networks. The claim that the test stays valid when checkpoint nodes are uncharacterized is the part that needs the most scrutiny. The abstract and stress-test note both flag that the nonlinearity is supposed to rule out other dynamics, yet without explicit bounds on what uncharacterized operations can produce in the two-population data, it is not obvious why mimicry is impossible. If the full derivation assumes fixed bases or limited noise models at the nodes, that should be stated clearly rather than left implicit. The citation pattern and math look standard for this subfield, with no obvious circularity or invented entities. This is the kind of paper experimental groups in quantum networks would want to see, because it targets a practical bottleneck. A serious referee should look at it, mainly to press on the uncharacterized-node claim and check whether the two-measurement data really separates transfer from alternatives. I would bring it to a reading group for the experimental part and the measurement reduction, but I would not cite it until the derivation is tightened.

Referee Report

2 major / 2 minor

Summary. The paper introduces a nonlinear criterion for identifying coherence transfer in quantum networks, derived from static and dynamic coherence features. It claims this criterion needs only two measurement settings on network-state populations in an experimental basis, works for arbitrary network size, and remains valid even with uncharacterized checkpoint nodes. The approach is presented as general across access levels, including no-input-change and time-domain dynamics cases. Experimentally, it demonstrates coherence transfer of single polarization qubits and polarization-entangled pairs in 4- and 6-photon entanglement networks via remote state preparation and entanglement swapping, offering evidence in multi-photon setups.

Significance. If the central derivation holds and the nonlinearity indeed excludes mimicry by uncharacterized node operations, this would be a useful practical advance for verifying coherence transfer in complex networks with minimal access and incomplete characterization. The experimental demonstration in multi-photon entanglement networks is a concrete strength, supporting applicability to quantum information tasks like entanglement distribution. The parameter-free aspect (two settings independent of size) and generality claims, if substantiated, add value for open quantum systems studies.

major comments (2)

[Theoretical section on the nonlinear criterion] § on the nonlinear criterion derivation: the claim that the criterion 'remains valid even when the verification capabilities of checkpoint nodes are uncharacterized' is load-bearing for the central result, yet the manuscript provides no explicit inequality, bound on node operations, or proof that the two observed populations cannot arise from unknown unitaries or noise at checkpoints without coherence transfer. The skeptic concern on separating transfer from mimicry in two-population data is not addressed with a concrete model or counterexample exclusion.
[Experimental results] Experimental section (4- and 6-photon networks): without the full data tables, error analysis, or details on how the two measurement settings were selected and applied (including any post-selection), it is impossible to verify if the reported evidence supports the criterion or if hidden assumptions about fixed bases affect the results. This directly impacts the experimental validation of the uncharacterized-node claim.

minor comments (2)

[Abstract] The abstract is information-dense; separating the theoretical criterion claims from the experimental demonstration would improve readability.
[Introduction] Notation for 'network-state populations in an experimental state basis' could be clarified with an explicit definition or example early in the text to aid readers unfamiliar with the setup.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its significance. We address each major comment point by point below, with clarifications and commitments to revision where the manuscript requires strengthening.

read point-by-point responses

Referee: [Theoretical section on the nonlinear criterion] § on the nonlinear criterion derivation: the claim that the criterion 'remains valid even when the verification capabilities of checkpoint nodes are uncharacterized' is load-bearing for the central result, yet the manuscript provides no explicit inequality, bound on node operations, or proof that the two observed populations cannot arise from unknown unitaries or noise at checkpoints without coherence transfer. The skeptic concern on separating transfer from mimicry in two-population data is not addressed with a concrete model or counterexample exclusion.

Authors: We acknowledge that the manuscript's theoretical section derives the nonlinear criterion from static and dynamic coherence features but does not include an explicit bound or counterexample proof excluding mimicry by arbitrary local operations at uncharacterized checkpoints. The two-population data is shown to violate the criterion only under coherence transfer in the presented derivation, yet a dedicated subsection with a concrete model (e.g., showing that any unitary or depolarizing noise at checkpoints preserves the bound unless transfer occurs) is indeed missing. We will add this explicit inequality and exclusion argument in the revised version to directly address the skeptic concern. revision: yes
Referee: [Experimental results] Experimental section (4- and 6-photon networks): without the full data tables, error analysis, or details on how the two measurement settings were selected and applied (including any post-selection), it is impossible to verify if the reported evidence supports the criterion or if hidden assumptions about fixed bases affect the results. This directly impacts the experimental validation of the uncharacterized-node claim.

Authors: We agree that the experimental section in the main text is summarized and lacks the complete data tables, error analysis, and explicit details on measurement selection and post-selection. The two settings were chosen as the computational and diagonal bases for population measurements in the experimental state basis, with post-selection limited to standard four-fold and six-fold coincidence events. Full tables, error propagation, and basis justification are in the supplementary material. We will expand the main experimental section to include a summary of these elements and clarify that no hidden assumptions on fixed bases beyond the reported entanglement swapping protocol affect the uncharacterized-node validation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of nonlinear coherence transfer criterion

full rationale

The paper presents a nonlinear criterion derived from static and dynamic coherence features for detecting transfer in quantum networks. It requires only two population measurements in an experimental basis and claims validity independent of network size or checkpoint characterization. No quoted equations or steps in the provided abstract reduce the criterion to a self-definition, fitted input renamed as prediction, or load-bearing self-citation chain. The derivation is presented as general and independent, with experimental validation via remote state preparation and entanglement swapping in multi-photon networks. This is a standard non-circular outcome for a criterion-introduction paper whose central claim does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are specified in the abstract; the criterion is described at a high level without detailing underlying assumptions or fitted quantities.

pith-pipeline@v0.9.0 · 5465 in / 1155 out tokens · 54259 ms · 2026-05-10T06:43:42.072712+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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at Claire, which acts as the check- point operationE V. After the BSs and postselection onto the subspace with exactly one particle per party, the nor- malized state becomes: |ψpost⟩= 1 2 h a† 1 b† 1c† 1 +b † 2c† 2 +a † 2 b† 2c† 1 +b † 1c† 2 i |0⟩.(S4) Each party records which output port was clicked, iden- tifying detector 1 as having outcome 0 and detec...
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(|H1V2H3V4⟩+|V 1H2V3H4⟩), where the subscripts represent the mode numbers, whereas the second photonic fusion process produced the state|G 4⟩= (1/ √
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These four-photon state fidelities indicate the perfor- mance of coherence transfer in the multi-photon entan- gled networks we have created

(|H1V2V5H6⟩+|V 1H2H5V6⟩). These four-photon state fidelities indicate the perfor- mance of coherence transfer in the multi-photon entan- gled networks we have created. On the other hand, in order to verify that the source indeed generates gen- uine six-photon entanglement, we evaluate the entangle- ment witness associated with the six-qubit GHZ state |G6⟩= (1/ √
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Coherence input. We implement the RSP proto- col to input a stateρ in,k, which is the post-measurement state of the input node, performed by the input node holder Alice, who implements the processE RSP accord- ing to the target operationU † and the followedZmea- surement in the basis{|i⟩}={|0⟩=|H⟩,|1⟩=|V⟩}. Photons 2 and 6 are measured to determine the in...
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To transmit the input state further in a four-photon entanglement network for N= 4 [Fig

The evolution of coherence. To transmit the input state further in a four-photon entanglement network for N= 4 [Fig. S5(a)], we perform a photonic fusion ˜Efusion of photon 1, which is in the state after RSP at node 2, and photon 3 at node 3, along with theXmeasurements in the basis{|+⟩,|−⟩}for both photons, considering the events where the post-measureme...
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We measure photon 4 at the output checkpoint nodes 4 and 6 in the output states of the four-photon [Fig

Output of coherence. We measure photon 4 at the output checkpoint nodes 4 and 6 in the output states of the four-photon [Fig. S5(a)] and six-photon [Fig. S5(b)] entanglement networks,ρ out,k, respectively, according to the introduced criterion. We perform the population measurement (Zmeasurement) on the stateρ out,k to ob- tain the diagonal elements of th...
[55]

Detection of coherence transfer. With regarding the experimental probabilitiesρ (d) out,k andP EV(i|ρout,k) for both experimental coherence transfer processes in the cases ofN= 4 andN= 6, we analyze the experimental transfer process using the introduced criterion, Eq. (1) in the main text. To conduct a comprehensive transfer assessment, we employ the SDP ...
[56]

Onto the states:{|ϕ +⟩,|ϕ −⟩} A photonic fusion operation can effectively project onto the Bell basis [21, 27, 28]. However, in practical applications, implementing BSM with linear optics faces fundamental limitations: out of the four Bell states, only two can be reliably distinguished in a single setup us- ing a PBS and photon detectors. The PBS operator...
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Onto the states:{|ψ +⟩,|ψ −⟩} We now examine a different configuration of the PBS that allows the BSM to project onto the Bell states|ψ +⟩ 12 HWPQWPPBSHWPQWPPBS (a) (b) FIG. S8. PBS-based BSM. (a) The first PBS configuration enables the BSM to project onto the Bell states|ϕ +⟩or |ϕ−⟩. The waveplates configuration at the output modes c and d, together with...
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Meanwhile, the entanglement between nodes ensures the transfer of co- herence to a subsequent pair, even without direct inter- action between them

From a coherence-transfer perspective, the coherence of the Bell states is input via the BSM. Meanwhile, the entanglement between nodes ensures the transfer of co- herence to a subsequent pair, even without direct inter- action between them. This is an entanglement-swapping [20, 29, 30] process that confirms that entanglement has been successfully swapped...
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We imple- ment the BSM protocol to input a stateρ in,k with Bell- state coherence, which is the post-measurement state of the input node, measured by two input node holders

Input and the evolution of coherence. We imple- ment the BSM protocol to input a stateρ in,k with Bell- state coherence, which is the post-measurement state of the input node, measured by two input node holders. BSMs are carried out on photons 1 and 3 [Fig. S9(a)]. We aim to input the following states in the ordering: ρin,1 =|ψ +⟩⟨ψ+|, ρin,2 =|ψ −⟩⟨ψ−|,(S...
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In an ideal scenario, we an- ticipate observing the following output states

Output of coherence. In an ideal scenario, we an- ticipate observing the following output states. ρout,1 =|ψ +⟩⟨ψ+|, ρout,2 =|ψ −⟩⟨ψ−|,(S35) ρout,3 =|ϕ +⟩⟨ϕ+|, ρout,4 =|ϕ −⟩⟨ϕ−|. We measure photons (2,4) at the output checkpoint nodes (2,4), and photons (6,4) at the output checkpoint nodes (6,4) in the output states of the four-photon [Fig. S9(a)] and six...
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Detection of coherence. With regarding the ex- perimental probabilitiesρ (d) out,k andP EV(i|ρout,k) for both experimental coherence transfer processes in the cases ofN= 4 andN= 6, we analyze the experimental transfer process using the introduced criterion. To con- duct a comprehensive transfer assessment, we employ the SDP technique to find the minimum v...
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The transferred coherence of the Bell states of photons 2 and 4, introduced by BSM, is further disrupted by polarizers (Pol.) placed along their respective paths

Control experiments. The transferred coherence of the Bell states of photons 2 and 4, introduced by BSM, is further disrupted by polarizers (Pol.) placed along their respective paths. For bothN= 4 [Fig. S9(b)] andN= 6 [Fig. S10(b)], this process is considered incapable of co- herence transfer and is represented byE Net,2. See also Fig. S11 (N= 4) and Fig....
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Coherence transfer in multi-photon entanglement networks. As previously discussed, the three entangled photon pairs are combined using Photonic fusion units 1 and 2 to create a six-photon GHZ state, which has been verified as a reliable backbone for a quantum net- work [14]. In this context, since the GHZ state and the star graph state are equivalent with...
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Our experiments demonstrate the general method of inputting quantum information used in entanglement networks [14]

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