Assessment of Polarization Entanglement Source: Photon Counting and Correlation Measurement

Josef Bla\v{z}ej; Josef Vojt\v{e}ch; Martin Guldan; Tom\'a\v{s} Nov\'ak

REVIEW 4 major objections 6 minor 6 references

Assessment of Polarization Entanglement Source: Photon Counting and Correlation Measurement

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that a one-sided coincidence entropy computed from linear-polarization coincidence counts alone tracks the degree of entanglement of telecom photon sources, offering a cheaper certification route than quantum state…

desk verdict A useful direct-measurement entanglement metric with a sound central idea, but the three-source, no-background validation doesn't yet support the 'corresponds well' claim. read the letter →

arxiv 2505.23979 v1 pith:YCRXQGB4 submitted 2025-05-29 quant-ph

Tomáš Novák , Martin Guldan , Josef Vojtěch , Josef Blažej This is my paper

classification quant-ph

keywords polarizationentanglementphotoncountingcoincidencemeasurementone-sidedentropydegreeofquantumstatetomographytelecommunicationbiterrorrate

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

The paper sets out a measurement procedure for certifying commercial polarization-entanglement photon sources at telecommunication wavelengths, using photon counting and coincidence statistics rather than full quantum state tomography. Its central proposal is a one-sided coincidence entropy computed from coincidence counts in the linear polarization bases only, defined so that the horizontal/vertical and diagonal/antidiagonal bases enter as mutually unbiased. Across three sources, this entropy falls as QST purity falls (7.30, 6.88, and 5.07/4.89 for purities 0.89, 0.86, and 0.61), and the paper takes this as evidence that the entropy tracks the degree of entanglement. The paper also models how detector dead time, saturation, and fiber dispersion distort single and coincidence counts, because those non-idealities cap the signal-to-noise ratio and feed directly into quantum bit error rate.

What carries the argument

The load-bearing object is the one-sided coincidence entropy of Eq. (4): for each linear polarization $j\in\{H,V,D,A\}$, the same-basis pair $(jj,jk)$ and the cross-basis pair $(jl,jm)$ with 45-degree-rotated polarizations are normalized to binary probability distributions, and $H$ is the sum over $j$ of binary-entropy terms $H(p_1,p_2)=-p_1\log_2 p_1-p_2\log_2 p_2$ for same and cross coincidence counts. Its one-sided version, evaluated for Alice or Bob alone, is bounded above by 8 and needs only linear-basis coincidence counts, which removes the circular-basis projections that QST requires. The supporting machinery is the dead-time saturation model for detectors, which gives the expected single and coincidence rates as functions of detector efficiency, dead time, and incident rate, and supplies the false-coincidence estimate $R_M^2\Delta t$ that sets the signal-to-noise limit.

What would settle it

Measure $H$ for a source with known QST purity while widening the coincidence window or adding uncorrelated background light; if $H$ shifts significantly while QST purity stays fixed, or if the ranking of sources by $H$ changes after subtracting accidental coincidences, then $H$ is not a faithful entanglement measure.

Watch

Extended reading notes

Core claim

The paper claims that the degree of polarization entanglement of a telecom photon source can be read off from ordinary coincidence measurements without reconstructing the density matrix. The readout is the one-sided coincidence entropy $H$, defined for Alice and Bob separately by applying the binary entropy function to normalized same-basis and cross-basis coincidence probabilities in the H/V and D/A settings; the cross terms are included so the two linear bases enter as mutually unbiased, a property that QBER lacks. In the measured sources, $H$ decreases with decreasing QST purity and with decreasing polarization visibility, while the difference between maximal and minimal single-photon visibility tracks entanglement better than either visibility alone. The paper concludes that $H$ is suitable for quantum communication monitoring because it needs no circular-basis measurements and its 16 components could reveal adversary interference.

Load-bearing premise

The claim that the one-sided coincidence entropy tracks the true degree of entanglement assumes that accidental coincidences and detector dark counts are small enough that the raw coincidence counts stand in for the true polarization correlations.

Editorial extensions

If this is right

A source can be screened for entanglement quality with only linear-basis coincidence counts, so certification tests become faster and require no circular waveplates.
The one-sided entropy values $H_A$ and $H_B$, together with their 16 component terms, can serve as a live monitor of a quantum link, flagging drift or adversarial interference in the polarization channel.
The measured ordering of $H$ against QST purity means the entropy can serve as a scalar quality figure when full tomography is impractical.
Operating sources below detector saturation with a small coincidence window keeps the true-to-false coincidence ratio high and directly bounds the achievable QBER.

Reading between the lines

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

Since the entropy in Eq. (4) is defined on normalized raw counts, a natural next test is whether $H$ remains faithful when accidental coincidences are subtracted; if it does, tomography-free monitoring becomes still more reliable in noisy deployed fiber.
The construction only needs mutually unbiased measurement pairs, so the same entropy idea could be transferred to time-bin or frequency-bin entangled sources by substituting the appropriate unbiased bases.
The paper's own dispersion measurement implies that $H$ and visibility should be certified at the receiver end after fiber transmission, not only at the source output, for deployed quantum links.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First, what's new. The one-sided coincidence entropy H in Eq. (4), combining same-basis and cross-basis terms over HV and DA, looks original. It is computable from linear-basis coincidence counts alone, with no QST and no circular basis, so it is genuinely attractive for telecom QKD monitoring. The paper also does honest work on detector saturation and dead-time behavior, including the counterintuitive coincidence rise under attenuation and the dispersion broadening over 28 km of fiber.

The strength is real: H is defined independently of QST, with no fitting to QST metrics, so Table 1 is a genuine empirical comparison, not a circular one. The ordering of H values does track the three sources' purities and QBERs. That is promising, and the reader's low circularity score is right.

The soft spots are exactly where the stress-test lands. The whole validation is one table with three sources, no error bars, and no subtraction of accidental coincidences. As estimated from raw counts, H is biased toward 1/2 by any constant background, and that bias hits high-purity sources hardest. For the 3 nm C-band source, QBER=0.19 means roughly 19% wrong-basis coincidences, so the background is not plausibly negligible there; and in Fig. 3 the authors themselves subtract a 350-count/bin floor with S/N around 1/3, showing that backgrounds in this setup are known to be significant. Without accidental-coincidence subtraction or a demonstration that false coincidences are negligible, the H gaps (7.30, 6.88, 5.07) could be within background uncertainty. The authors also admit their model deviates in low dead-time and high saturation regimes, and they defer the algebraic correspondence between H and QST to future work. That leaves Table 1 carrying the entire validation, so the 'correspond well' phrasing is stronger than the evidence.

The single-photon visibility discussion is actually a credit: they test their own hypothesis and conclude it is likely incorrect. That is the right way to handle a candidate metric.

Who is this for: groups certifying or monitoring telecom polarization-entanglement sources who want a cheap, continuous statistic. It deserves a serious referee, but the referee should require a proper background treatment and error analysis for Table 1, and ideally more than three sources, before the correspondence claim is accepted. I would engage with it and ask for revision, not desk-reject it.

Referee Report

4 major / 6 minor

Summary. The paper presents a measurement framework for characterizing commercial polarization-entanglement sources at telecommunication wavelengths. It combines photon-counting rate models, coincidence measurements, polarization visibility, QST metrics, and a proposed one-sided coincidence entropy H defined in Eq. (4) from coincidence counts in linear polarization bases. The central claim, stated in Sec. 7, is that direct-measurement metrics, especially H, correspond well with QST-derived metrics of the degree of entanglement, based on Table 1 for three commercial sources. The paper also reports detector saturation and dispersion effects and suggests that H could serve as a simpler monitoring statistic for quantum communication.

Significance. If the claimed correspondence holds, the coincidence entropy H would be a practically useful, parameter-free metric computable from linear-basis coincidence counts alone, without requiring full QST; this would be a genuine simplification for source certification and link monitoring. The paper provides concrete measurements on three commercial sources and explicitly acknowledges limitations of the rate models in saturation regimes, which is commendable. I find no circularity in the definition of H: it is computed from coincidence counts and no parameter is fitted to the QST metrics. However, the empirical validation is currently fragile because the reported H values lack uncertainty estimates and because the underlying coincidence counts are not corrected for accidental coincidences and dark counts, despite evidence in the paper itself that such backgrounds are significant. The significance is therefore conditional on strengthening the data analysis.

major comments (4)

[Eq. (4), §5] The definition of the probabilities in Eq. (4) mixes theoretical state amplitudes with measured quantities: p_jj is written as |⟨jj|Ψ⟩|²/N_same_j and N_same_j is also defined from amplitudes. For the direct measurement claim in Table 1, it must be specified whether N_same_j and N_cross_j are the measured sums of coincidence counts or are computed from the QST-reconstructed density matrix. If the former, the formulas should be written explicitly as count ratios C_jj/(C_jj+C_jk); if the latter, H is not a direct measurement metric. This ambiguity affects the interpretation of every H value in Table 1.
[Table 1, §7] The central validation claim that direct-measurement metrics 'correspond well' with QST metrics is not supported by the data as presented: there are only three sources, and none of the reported values (p, S, ΥA, V_HV, V_DA, QBER, H_A, H_B, SV_max, SV_min) carry error bars or confidence intervals. The H ordering 7.30, 6.88, 5.07/4.89 could be within measurement uncertainty, and no quantitative measure of agreement (e.g., a correlation coefficient with uncertainty or a calibration residual) is provided. Please report uncertainties from repeated measurements and a statistical comparison.
[Eq. (4), Table 1, Fig. 3] The H values in Table 1 appear to be computed from raw coincidence counts without subtracting accidental coincidences or dark counts, although the authors' own Fig. 3 shows a 350-count/bin background floor with S/N≈1/3 and the 3 nm C-band source in Table 1 has QBER=0.19. A constant background added to each coincidence setting biases every estimated probability toward 1/2 and systematically lowers H_same, with the largest effect on the highest-purity sources. Until accidental coincidences are subtracted (or shown to be negligible compared with true coincidences in all three sources), the claimed correspondence between H and the QST degree of entanglement cannot be distinguished from a background artifact.
[§7, Conclusions] The statement that the difference SV_max − SV_min 'appears to depend on the degree of entanglement' and the resulting rejection of the circularity-of-impurity hypothesis are based on a qualitative inspection of three rows in Table 1. If this secondary conclusion is retained, it needs a quantitative analysis with uncertainties; otherwise it should be presented as a tentative observation rather than a conclusion.

minor comments (6)

[Abstract] The phrase 'for a three commercially available sources' should read 'for three commercially available sources'.
[§4, Fig. 3] Please clarify whether the 350-count/bin subtraction was applied to any data entering Table 1, and if not, explain how the S/N estimate relates to the measurements used for H.
[§5, Eq. (4)] The symbol H is used both for the total coincidence entropy and for the binary entropy H(p1,p2) in Eq. (4); using a different symbol for the binary entropy (e.g., h_bin) would remove the ambiguity.
[§5] The term 'one-sided coincidence entropy' is not defined; please clarify whether H_A and H_B refer to measurements in Alice's and Bob's arms and how they differ operationally.
[Table 1] For the C-band (3 nm) source, H_A=5.07 and H_B=4.89 differ; the paper does not discuss whether this asymmetry is physical or due to setup asymmetry.
[§7] The deviations of single-photon counts from Eq. (1) at low dead-times and of coincidences from Eq. (2) at high saturation are described but not quantified; for a framework claiming comprehensiveness, provide fit residuals or error bars for these model comparisons.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: coincidence entropy H is an independent statistic compared empirically with QST metrics.

full rationale

The paper's central comparison is between one-sided coincidence entropy H (Eq. 4), computed directly from coincidence counts in linear bases, and QST-derived purity, Von Neumann entropy, and Rényi entropy. H is defined from measured counts without any parameter fitted to QST values, so the Table 1 correlation is an empirical validation rather than a construction. The only caveat is the lack of accidental-coincidence subtraction, which affects measurement accuracy but not circularity. No load-bearing self-citations appear; the cited references are standard methods or external results. The algebraic correspondence between H and QST metrics is explicitly deferred to future work, so the paper does not claim to derive H from QST. Hence no circular step can be quoted.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central validation depends on three domain assumptions and one ad hoc display parameter. The most consequential is that raw coincidence counts, without accidental subtraction, faithfully represent the probabilities in Eq. (4). The H metric is not circular but is unproven as an entanglement monotone.

free parameters (1)

accidental-coincidence floor subtracted in Fig. 3 = 350 counts/bin
Chosen ad hoc to improve figure representation; the floor is not independently measured, and it directly affects the quoted S/N of ~1/3.

assumptions (3)

domain assumption Detector response follows the dead-time model of Eq. (1) with independent photon arrivals.
Used to estimate single and coincidence rates in Section 3; the paper itself notes deviations at low dead-times and high saturation.
ad hoc to paper The entropy H defined in Eq. (4) is a valid monotonic surrogate for the degree of entanglement.
No proof or prior reference is given; the claim is supported only by three measured sources in Table 1.
domain assumption Background and accidental coincidences are negligible in the normalization of probabilities in Eq. (4).
The paper discusses false coincidences in Section 3 but does not subtract them from the metrics in Table 1.

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Cite this review

Pith. "Pith review of Assessment of Polarization Entanglement Source: Photon Counting and Correlation Measurement." pith.science (2026). https://pith.science/paper/YCRXQGB4

@misc{pith2026250523979,
  author       = {Pith},
  title        = {Pith review of: Assessment of Polarization Entanglement Source: Photon Counting and Correlation Measurement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YCRXQGB4}},
  note         = {Machine review of arXiv:2505.23979}
}

read the original abstract

Commercial sources of polarization entanglement at telecommunication wavelengths are already available on the market, but they lack proper certification or third-party testing. We aim to provide a comprehensive testing framework for photon counting and correlation measurements to characterize the parameters of these sources in a scalable and repeatable manner. The detection setup is included in our considerations, as the non-idealities of the components negatively affect the relevance of the measurement results. We discuss bounds for both true and false coincidences with rigorous probabilistic approach, as their ratio directly impacts the resolution of coincidence measurements and is reflected in Quantum Bit Error Rate (QBER) in the quantum telecommunication system. Quantum State Tomography (QST), polarization visibility measurements, temporal correlations measurements, and computations of other statistics are to be performed and compared at the state-of-the-art level for a three commercially available sources. Given that QST is demanding in terms of number of measurements and post-processing analysis, we discuss the relevance of determining the degree of polarization entanglement considering solely other statistics of direct measurement approach.

Figures

Figures reproduced from arXiv: 2505.23979 by the authors.

**Figure 2.** Coincidences and single counts as function of attenuation on both detection arms. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Correlations broadening due to dispersion in single-mode silica fibers of 60 nm broadband C-band [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Measured visibility of 100 nm broadband O-band source in the Bell state [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Measured maximal and minimal single-photon visibilities of 60 nm broadband C-band source. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: Reconstructed density matrix from QST of 60 nm broadband C-band source. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

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Reference graph

Works this paper leans on

6 extracted references · 5 canonical work pages

[1]

James, D. F. V., Kwiat, P. G., Munro, W. J., and White, A. G., ``Measurement of qubits,'' Phys. Rev. A 64 , 052312 (2001)

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[3]

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[4]

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Shi, Y., Moe Thar, S., Poh, H. S., Grieve, J. A., Kurtsiefer, C., and Ling, A., ``Stable polarization entanglement based quantum key distribution over a deployed metropolitan fiber,'' Applied Physics Letters 117 (12), 124002 (2020)

work page 2020
[5]

A., Dashkasan, J

Motazedifard, A., Madani, S. A., Dashkasan, J. J., and Vayaghan, N. S., ``Nonlocal realism tests and quantum state tomography in sagnac-based type-ii polarization-entanglement spdc-source,'' Heliyon 7 (6), e07384 (2021)

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[6]

write newline

" write newline "" before.all 'output.state := FUNCTION blank.sep after.quote 'output.state := FUNCTION fin.entry output.state after.quoted.block = 'skip 'add.period if write newline FUNCTION new.block output.state before.all = 'skip output.state after.quote = after.quoted.block 'output.state := after.block 'output.state := if if FUNCTION new.sentence out...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

James, D. F. V., Kwiat, P. G., Munro, W. J., and White, A. G., ``Measurement of qubits,'' Phys. Rev. A 64 , 052312 (2001)

work page 2001

[2] [2]

F., ``Radiation detection and measurement,'' (1999)

Knoll, G. F., ``Radiation detection and measurement,'' (1999)

work page 1999

[3] [3]

Jin, R.-B., Shimizu, R., Wakui, K., Fujiwara, M., Yamashita, T., Miki, S., Terai, H., Wang, Z., and Sasaki, M., ``Pulsed sagnac polarization-entangled photon source with a ppktp crystal at telecom wavelength,'' Optics Express 22 (10), 11498--11507 (2014)

work page 2014

[4] [4]

S., Grieve, J

Shi, Y., Moe Thar, S., Poh, H. S., Grieve, J. A., Kurtsiefer, C., and Ling, A., ``Stable polarization entanglement based quantum key distribution over a deployed metropolitan fiber,'' Applied Physics Letters 117 (12), 124002 (2020)

work page 2020

[5] [5]

A., Dashkasan, J

Motazedifard, A., Madani, S. A., Dashkasan, J. J., and Vayaghan, N. S., ``Nonlocal realism tests and quantum state tomography in sagnac-based type-ii polarization-entanglement spdc-source,'' Heliyon 7 (6), e07384 (2021)

work page 2021

[6] [6]

write newline

" write newline "" before.all 'output.state := FUNCTION blank.sep after.quote 'output.state := FUNCTION fin.entry output.state after.quoted.block = 'skip 'add.period if write newline FUNCTION new.block output.state before.all = 'skip output.state after.quote = after.quoted.block 'output.state := after.block 'output.state := if if FUNCTION new.sentence out...