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REVIEW 3 major objections 5 minor 1 cited by

Single-click protocols for remote state preparation using weak coherent pulses

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper shows that remote state preparation with weak coherent pulses can use a single-click protocol that matches double-click fidelity while achieving a higher rate, plus a two-click variant that relaxes phase-stabilization demands.

desk verdict Useful protocol paper with real analytic results; abstract overstates SC's regime of validity until phase noise is accounted for. read the letter →

arxiv 2508.14857 v1 pith:235DECAV submitted 2025-08-20 quant-ph

Janice van Dam , Emil R. Hellebek , Tzula B. Propp , Junior R. Gonzales-Ureta , Anders S. S{o}rensen , Stephanie D.C. Wehner This is my paper · ORCID
classification quant-ph
keywords remotestatepreparationweakcoherentpulsessingle-clickprotocoldouble-clickquantumrepeatersphasenoisemeasurement-device-independentQKDblindcomputing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Remote state preparation allows a low-resource client to place a known quantum state on a server's qubit using entanglement. This paper claims that when the client uses weak coherent pulses instead of true single photons, a single-click protocol—where only one photon must reach the intermediate Bell measurement—prepares the target state at the same leading-order fidelity as the standard double-click protocol while achieving a higher success rate. It also proposes a double-single-click variant that repeats the single-click step twice and applies a controlled-NOT gate, exchanging some fidelity for reduced phase-stabilization requirements. If right, these protocols let quantum-network clients trade hardware simplicity for speed without the fidelity penalty that single-click schemes pay in ordinary entanglement generation.

What carries the argument

The object that carries the argument is the click pattern at the Bell state measurement and the encoding that produces it. DC uses a two-mode encoding (polarization or time-bin) and needs a click in both modes; SC uses presence-absence encoding in a single mode, so one click on either output detector of a 50:50 beamsplitter heralds success, and the balance between client and server photon arrival probabilities is set by the server's bright-state parameter ξ. DSC repeats the SC round twice and applies a CNOT gate followed by a measurement, so the final phase is the difference of the two single-click phases, deleting any common phase drift. The phase-noise model then enters as a Gaussian σ wit

What would settle it

On a fixed link with known client and server efficiencies and active phase stabilization, measure the accepted-state rate and fidelity of SC and DC as the client intensity is varied. The central claim fails if DC produces more accepted states per unit time than SC at the same fidelity (for example at F=0.98), or if the measured SC infidelity grows faster than ηc(4−3ηs)/(16ηs)|α|² in the small-|α|² regime, since that would indicate the leading-order error model is missing a contribution.

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Extended reading notes

Core claim

The central claim is that single-click RSP is not merely faster than double-click RSP—it matches its fidelity to leading order. For a client amplitude α, client channel efficiency ηc, and server emission efficiency ηs, the SC and DC infidelities in the small-intensity limit are both ηc(4−3ηs)/(16ηs)|α|², while the dimensionless rates scale as 2ηc|α|² (SC) versus ηcηs|α|²/2 (DC), so SC strictly dominates DC whenever its phase noise is low enough to reach the target fidelity. DSC, which runs SC twice and then applies a CNOT gate, has twice the leading-order infidelity of SC/DC but still outperforms DC in rate, and it cancels the random overall phase so that only phase drift between the two cli

Load-bearing premise

The advantages claimed for SC and DSC rest on the client's optical phase being stable—over one attempt for SC, over the interval between two successful clicks for DSC—because phase noise sets a fidelity ceiling of (1+e^{-σ²/2})/2 that DC does not have.

Editorial extensions

If this is right

  • With active phase stabilization, SC supplies more remote-state-preparation successes per unit time than DC at the same target fidelity, which directly increases the rate of protocols built on RSP.
  • DSC removes the need for an active phase-stabilization servo when two SC successes occur within the phase-coherence time, and still beats DC's rate in some regimes.
  • In a repeater-chain QKD setting, the SC-based variant is equivalent to a twin-field-type protocol in the noiseless limit and can be analyzed with existing measurement-device-independent security proofs.
  • For applications needing several remotely prepared qubits, the higher rate of SC/DSC can beat DC on overall fidelity because slower preparation gives memory decoherence more time to act.
  • A composable security proof for blind quantum computing with SC is still missing; DSC may be easier to prove secure because its final phase is a phase difference, so phase randomization of both pulses is compatible.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper restricts attention to equatorial states; adjusting the client intensity and the server bright-state parameter should extend SC to arbitrary latitudes without changing the single-click mechanism, giving a direct experimental handle the authors chose not to explore.
  • A simple pre-screening rule follows from the phase-noise ceiling: if an interferometric measurement of the client's phase shows σ above about 0.5 rad, SC cannot supply 0.98-fidelity states and the comparison should be made against DC at lower fidelity targets.
  • End-to-end repeater performance is not quantified here; one obvious next calculation is to include memory cutoff times and decoherence between the two DSC clicks, which the paper explicitly flags as an upper-bound assumption.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper considers remote state preparation (RSP) with a client that uses weak coherent pulses (WCPs). It introduces two protocols—single-click (SC) and double-single-click (DSC)—and compares them with the previously known double-click (DC) protocol. The authors derive analytical expressions for the success rate and fidelity of all three protocols under loss, optimize the server's bright-state parameter ξ, and model Gaussian phase noise. Their central finding is that, to leading order in the client mean photon number |α|², SC and DC attain the same infidelity, while SC's rate scales as 2ηc|α|² versus ηcηs|α|²/2 for DC; DSC has twice the infidelity of SC/DC but a rate of 4ηc|α|²/3. The paper also discusses phase-noise limitations, compares protocols in rate–fidelity trade-off plots, and sketches an application to QKD over repeater chains, with a reduction to the CAL19 twin-field security proof in the appendix.

Significance. The main insight—that replacing a double-click with a single-click RSP does not incur an inherent fidelity penalty as it does in entanglement generation—is valuable and, if correct, has practical implications for quantum network clients with WCP sources. The analytical formulas are detailed enough to be checked, and the authors are transparent about some limitations (notably that the DSC fidelity is an upper bound because memory decoherence is omitted). The paper includes explicit derivations for the SC protocol, an optimized bright-state parameter, and a phase-noise model, which are useful contributions. However, the strength of the headline claim depends on a phase-noise regime that is not quantitatively grounded, and there is an internal inconsistency in the DSC rate derivation. The QKD application is only a sketch, not a full security proof, but that is appropriately caveated.

major comments (3)
  1. [Section II E and Abstract] The claim that “SC consistently achieves higher rates than DC” is not valid for all target fidelities. Under the paper's own phase-noise model, the maximum SC fidelity is (1+e^{-σ_SC²/2})/2, so for F=0.99 one needs σ_SC≲0.20 rad. The paper uses σ_SC=0.5 rad in Fig. 2(b) and treats σ_SC as a free parameter without deriving an achievable value from Ref. [34]. Please state the residual phase noise demonstrated by Ref. [34], or explicitly qualify the abstract and Section III conclusions with the regime σ_SC below the threshold needed for the target fidelity.
  2. [Appendix A 3, Eq. (A17) vs Eq. (8)] The DSC rate derivation is internally inconsistent. Eq. (A17) defines p_SC as the single-click success probability with displacement α/√2, giving p_SC ≈ ηc|α|². Then RDSCτ ≈ (2/3)ηc|α|² P_CNOT, which cannot reproduce the leading-order 4/3 ηc|α|² in Eq. (8) for any P_CNOT ≤ 1. To match Eq. (8), p_SC must be the full-displacement success probability ≈2ηc|α|² and P_CNOT≈1. Either Eq. (A17) or Eq. (8) is wrong; please reconcile and correct the derivation.
  3. [Section II D and Section III] The DSC protocol's fidelity is explicitly an upper bound because memory decoherence between the two SC successes is neglected. However, the protocol-comparison plots and the conclusion that “DSC can also achieve higher rates than DC” use this upper bound. Since the waiting time between two successes can be long, decoherence may substantially reduce the actual DSC fidelity, potentially eliminating the claimed advantage in realistic regimes. Please either include a simple decoherence model (e.g., exponential fidelity decay with waiting time) or clearly restrict the DSC claims to the ideal-memory limit and state that the comparison is against an upper bound.
minor comments (5)
  1. [Section II C] The sentence “the fidelity of DC has twice the negative slope of SC in the small |α|² limit” contradicts Eqs. (1) and (5), which have the same leading coefficient ηc(4−3ηs)/(16ηs), and also contradicts Section III. Please correct this sentence.
  2. [Section II D and Appendix A 3] The post-selection condition after the CNOT in DSC is stated as measuring the target qubit in |0⟩ in the main text, but Appendix A 3 says the state is accepted only if the target qubit is in the bright state |1⟩. Please clarify which outcome is post-selected and ensure the derivation matches.
  3. [Section III] The sentence “first order contributions in |α|² are … ηc(4−3ηs)|α|/16ηs” should read |α|², not |α|. There are also formatting issues in Eqs. (1) and (7) where division slashes are missing in the displayed formulas.
  4. [Section II A] There is a typo: “beam splitter transformations transformations” should be “beam splitter transformations.” Other minor typos include “on;y” (Section III) and “boarder” (Section III) instead of “border.”
  5. [Appendix C] The QKD security reduction is a sketch, not a full proof. The appendix states that “a comparison of the performance of both protocols in noisy scenarios is left for future work.” Please make clear in the main text that the QKD claim is a compatibility argument, not a security proof with finite-key analysis.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the rate and fidelity results follow from an explicit coherent-state/loss/BSM/detector model with analytic optimization; no fitted input is renamed as a prediction and no load-bearing self-citation chain is used.

full rationale

The paper's central comparison (SC vs DC vs DSC) is derived from first principles in Appendix A: input coherent state with amplitude α, loss channels ηc/ηs, 50:50 beam-splitter transformations, and detector projectors. The bright-state parameter ξ is optimized analytically (Eq. A12), not fitted to data, and the fidelity and rate expressions (Eqs. 1,2,5,6,7,8) are obtained by direct calculation from the resulting density matrices. The SC rate advantage over DC is a quantitative consequence of these expressions rather than an input; while it is conceptually natural that a one-click protocol has a higher success probability than a two-click protocol, the paper does not define the result into existence—P_SC and P_DC are separately derived and the fidelity equality at leading order is nontrivial. The phase-noise treatment introduces σ_SC and σ_DSC as free parameters and explicitly states that σ_SC must be determined experimentally and that DSC does not combat phase noise, only the technical stabilization requirement; this is a scope/feasibility limitation, not circularity. Citations to the authors' patents [29,30] merely flag pending applications for the new protocols and carry no mathematical weight; the remaining references are to independent experimental work or prior protocol literature. No equation reduces by construction to the claimed result, and no fitted quantity is renamed as a prediction. The skeptical concern about phase-stabilization feasibility (σ_SC not benchmarked for high-fidelity targets) is a legitimate correctness/regime-of-validity question, but it is not a circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The analytical results assume an idealized server (perfect matter-photon entanglement, no memory decoherence), Gaussian phase noise, and a linear-optics BSM. The free parameters are the optimized bright-state probability and the phase-noise variances, which set the advantage regions. No new physical entities are introduced.

free parameters (3)
  • Bright state parameter ξ = ξ² ≈ ηc |α|²/ηs (SC); optimized for rate in DSC
    The server's emission probability is chosen analytically to balance photon arrival rates. The SC fidelity result depends on this optimization.
  • Phase noise σ_SC and σ_DSC = 0.5 rad used in Fig. 2; swept in Fig. 4
    Gaussian phase noise standard deviations are free parameters; the maximum SC/DSC fidelity is (1+e^{-σ²/2})/2, so advantage regions depend on them.
  • Mean photon number |α|² = swept from 0.001 to 0.5
    Client laser intensity is the control parameter defining the rate-fidelity trade-off in all plots.
assumptions (5)
  • domain assumption The server emits a single photon in the bright state with perfect fidelity; all hardware except losses and phase noise is ideal.
    Stated in Section II: 'Apart from phase noise and losses, we assume ideal hardware, thus excluding decoherence, gate imperfections, and infidelity in the server photon-matter state.'
  • ad hoc to paper Phase noise is Gaussian distributed with standard deviation σ, giving fidelity factor e^{-σ²/2}.
    Section II E models phase noise this way; the authors note a wrapped Gaussian gives the same result. This is a convenient model, not derived from a measured distribution.
  • domain assumption Losses act as beam-splitter losses with efficiencies ηc, ηs and the BSM is a 50/50 beamsplitter with threshold detectors.
    Standard linear-optics model used throughout Appendix A.
  • domain assumption In DSC, the first remotely prepared qubit does not decohere while the second is generated.
    The paper states in Section III that this gives an upper bound on DSC fidelity; it is an idealization.
  • ad hoc to paper The QKD security reduction assumes perfect efficiencies and photon-number-resolving detectors.
    Appendix C1 uses this idealization to map RSP-SC to CAL19; it does not cover the lossy threshold-detector protocol.

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Cite this review

Pith. "Pith review of Single-click protocols for remote state preparation using weak coherent pulses." pith.science (2026). https://pith.science/paper/235DECAV

@misc{pith2026250814857,
  author       = {Pith},
  title        = {Pith review of: Single-click protocols for remote state preparation using weak coherent pulses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/235DECAV}},
  note         = {Machine review of arXiv:2508.14857}
}
read the original abstract

Remote state preparation (RSP) allows one party to remotely prepare a known quantum state on another party's qubit using entanglement. This can be used in quantum networks to perform applications such as blind quantum computing or long-distance quantum key distribution (QKD) with quantum repeaters. Devices to perform RSP, referred to as a client, ideally have low hardware requirements, such as only sending photonic qubits. A weak coherent pulse source offers a practical alternative to true single-photon sources and is already widely used in QKD. Here, we introduce two new protocols to the previously known protocol for RSP with a weak-coherent-pulse-based device. The known technique uses a double-click (DC) protocol, where a photon from both the server and the client needs to reach an intermediate Bell state measurement. Here, we add to that a single-click (SC) RSP protocol, which requires only one photon to reach the Bell state measurement, allowing for better performance in certain regimes. In addition, we introduce a double-single-click (DSC) protocol, where the SC protocol is repeated twice, and a CNOT gate is applied between the resulting qubits. DSC mitigates the need for phase stabilization in certain regimes, lowering technical complexity while still improving performance compared to DC in some regimes. We compare these protocols in terms of fidelity and rate, finding that SC consistently achieves higher rates than DC and, interestingly, does not suffer from an inherently lower fidelity than the DC, as is the case for entanglement generation. Although SC provides stronger performance, DSC can still show performance improvements over DC, and it may have reduced technical complexity compared to SC. Lastly, we show how these protocols can be used in long-distance QKD using quantum repeaters.

Figures

Figures reproduced from arXiv: 2508.14857 by the authors.

Figure 1
Figure 1. This terminology is analogous to that used [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 1
Figure 1. FIG. 1: Diagram illustrating the three remote state [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Trade-offs between fidelity and rate for the three RSP protocols, (a) without phase noise and (b) with phase [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (6 more)
Figure 3
Figure 3. Figure 3: FIG. 3: Local operations in the DSC protocol: some [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4: Optimal RSP protocol — DC, DSC, or SC — for a given target fidelity or rate, across varying levels of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Schematic drawing of the repeater QKD [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Optimal RSP protocol — DC, DSC, or SC — for a given target fidelity, across varying levels of phase noise [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Optimal RSP protocol — DC, DSC, or SC — for a given target rate, across varying levels of phase noise [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Optimal RSP protocol — DC, DSC, or SC — for a given target rate, across varying levels of phase noise [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Verifiable blind quantum computing: Comparative analysis and design considerations for client architectures

    quant-ph 2026-07 accept novelty 5.0 of 10

    Among information-theoretic MBQC VBQC clients, measurement-based RSP and cavity-reflection emission clients are the strongest near-term defaults once noise-robust security, rate, errors, and hardware cost are weighed ...

Reference graph

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    With this, we are thus able to mitigate the need for phase stabilization if the phase stays constant between the two emissions, this is discussed in Section II E. A detailed analysis of the protocol leads to the expressions for fidelity and rate FDSC = 1 2  1 + ηsηc|α|2/4 1 − e− ηc |α|2 2 × 1h ηs 2 1 + ηc|α|2 2 + (1 − ηs) 1 − e− ηc |α|2 2 i   ∼ 1 − ηc...

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    This can be a polarizing beamsplitter in the case of polarization encoding, or a regular beamsplitter with delay line in the case of time-bin encoding

    Double-click For double-click, the client sends out a WCP with displacement α, lets it fall onto a beamsplitter and includes a phase shift for one of the arms. This can be a polarizing beamsplitter in the case of polarization encoding, or a regular beamsplitter with delay line...

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    ηs 2 1 + ηc|α|2 2 ! + (1 − ηs) 1 − e−ηc|α|2/2 # |1⟩ ⟨1| . We next find the denominator, PSC|+ PSC|+ = e−ηc|α|2/2

    Single-click The client sends out a coherent state with displacement α = |α|e−iθ. The server sends out a single photon when its memory qubit is in the bright state, denoted |1⟩ (and no photon otherwise). The probability of the server being in the bright state is dependent on t...

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    The state after the two successful clicks is ρsys = ρSC ⊗ ρSC, with ρSC as in Equation A10

    Double-single-click For double-single-click, the single-click protocol is performed twice. The state after the two successful clicks is ρsys = ρSC ⊗ ρSC, with ρSC as in Equation A10. Then, a controlled-NOT (CNOT) gate is performed on the two prepared qubits, followed by a meas...

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    (A20) The state after the heralding becomes ρSC = (1 − ξ2)ηc|α|2 + ηsξ2 ηc|α|2(1 − ηsξ2) + ηsξ2 |ξ⟩ ⟨ξ| + ηc|α|2ξ2(1 − ηs) ηc|α|2(1 − ηsξ2) + ηsξ2 |1⟩ ⟨1|

    Single-click with photon number resolving detectors If we assume photon number resolving detectors, for single click the transformation now reads ρsys → ρSC = ⟨1+|ρsys|1+⟩ tr[ ⟨1+|ρsys|1+⟩] , (A19) which leads to the probability of success of obtaining a click in the ”plus”-mo...

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    For SC the phase of the coherent state θ will change as it travels to the BSM

    Phase noise Phase noise in this system arises from different underlying causes in the three protocols. For SC the phase of the coherent state θ will change as it travels to the BSM. We will thus transform the coherent state to the density matrix |α|e−iθ |α|e−iθ → Z dδθpδθ |α|e...

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    In particular follow the security proof given by Curty-Azuma-Lo in the so-called CAL19 protocol [40]

    Single-click Here we show that our SC protocol for remote state preparation (RSP-SC) in combination with the setup depicted in Figure5 can be used to implement a twin-field type protocol [20]. In particular follow the security proof given by Curty-Azuma-Lo in the so-called CAL...

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    The same is repeated on Bob’s side. (iv) The entanglement is propagated through the repeater chain using entanglement swapping until Alice’s and Bob’s registers share this state with neighboring nodes, such as S2 and SB. Then, a BSM is performed on S2 and SB of |ψA,S2 ⊗ ψB,SB ...

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    Double-click In this protocol, Alice and Bob send out BB84 states [41]. In the fictious entanglement-based protocol, for the Z basis, Alice and Bob start with a state ψA/B = 1√ 2 (|0, αa⟩ + |1, αb⟩) (C4) with αa/b = e−|α|2 P∞ n=0 αn √ n! (a†/b†)n |0⟩, where a† and b† are the c...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.