Random entanglement percolation on realistic quantum networks

Alessandro Romancino

REVIEW 2 major objections 4 minor 21 references

Random entanglement percolation on realistic quantum networks

T0 review · 2 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that in photonic quantum networks, polarization-dependent loss induces a known distribution of singlet-conversion probabilities via X(P) = 2/(1+10^(P/10)), and that the mean of this distribution alone sets the classical pe

desk verdict A correct but narrowly-scoped PDL-to-SCP map; the paper would be stronger if it acknowledged the geometry dependence. read the letter →

arxiv 2604.21967 v2 pith:JRWZILY5 submitted 2026-04-23 quant-ph

Alessandro Romancino This is my paper · ORCID

classification quant-ph

keywords entanglementpercolationquantumnetworkspolarization-dependentlosssingletconversionprobabilityrandomdisorderfiber-opticlinkscommunication

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

This paper builds on the idea that real quantum networks are heterogeneous, with each link having a different chance of yielding a singlet. It aims to show that polarization-dependent loss (PDL) in photonic fiber links naturally produces that heterogeneity, via a simple map from decibel loss to singlet-conversion probability (SCP): for a Bell pair that undergoes one-sided loss, X(P) = 2/(1 + 10^(P/10)). From this map, any distribution of PDL across links is converted into an SCP distribution, and the author derives the explicit density transformation and a weak-loss linear approximation. The reason this matters is that classical percolation depends only on the mean SCP, while the quantum percolation protocol (q-swaps) depends on the whole distribution through E[X_min]; PDL therefore gives a physically measurable knob for both thresholds. For three standard fiber PDL models, the computed average SCP lands near 0.71–0.75, above typical percolation thresholds.

What carries the argument

The central object is the map X(P) from PDL magnitude in decibels to edge SCP, together with its associated density transformation Eq. (4): f_X(x) = f_P[10 log10((2−x)/x)] · (20/ln10) · 1/[x(2−x)]. This map turns any physically motivated PDL distribution into an edge-SCP distribution. Combined with the identity E[X_min] = μ − 1/2 Δ, it connects measurable fiber statistics to entanglement percolation thresholds — RCEP through μ, RQEP through E[X_min].

What would settle it

Take a polarization-entangled source, send one photon through a variable PDL element while the other is untouched, measure the SCP of the post-selected pairs, and compare to X(P)=2/(1+10^(P/10)). A systematic deviation at known PDL, or a shift when both photons pass through the element, would falsify the map.

Watch

Extended reading notes

Core claim

The central claim is that random edge entanglement in photonic quantum networks is physically produced by polarization-dependent loss. Starting from a Bell state |Φ+⟩, PDL acts effectively as a local filter on one qubit; after postselection, the singlet-conversion probability is X = 2η2/(η1+η2), which becomes X(P)=2/(1+10^(P/10)) when expressed in decibels. Therefore any PDL distribution f_P induces an SCP density given by Eq. (4): f_X(x) = f_P[10 log10((2−x)/x)] · (20/ln10) · 1/[x(2−x)]. The paper then connects this map to percolation: random classical entanglement percolation depends only on the mean μ, while random quantum entanglement percolation after q-swaps depends on E[X_min] = μ − 1

Load-bearing premise

PDL acts as a one-sided local filter on a pure Bell pair, so after postselection the state stays pure and SCP = 2η2/(η1+η2); if both photons suffer PDL or decoherence enters, the mapping changes.

Editorial extensions

If this is right

RCEP in a PDL-limited photonic network is determined only by the average SCP μ; for the three studied PDL models μ ≈ 0.714, 0.739, and 0.755, giving explicit operating points.
RQEP depends on the shape of the PDL distribution through E[X_min], so two photonic networks with identical mean losses can behave differently under q-swap preprocessing.
In the weak-PDL regime, the linear relation E[X] = 1 − (ln10/20)E[P] allows a quick estimate of the percolation threshold from the average PDL alone.
The density transformation means the full SCP distribution for any PDL model can be tabulated without simulating the quantum state.
PDL provides a concrete physical mechanism for the random edge disorder assumed in random entanglement percolation, bridging theory and deployed fiber links.

Reading between the lines

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

If PDL affects both photons of a pair rather than acting as a one-sided filter, the map X(P) would change; the paper's formulas are testable against that two-sided-loss scenario.
The paper treats each edge as present with SCP X, omitting the probability that the pair is lost entirely; including survival probabilities would likely raise percolation thresholds.
The map could be inverted: measuring the SCP distribution at network nodes would estimate the underlying PDL statistics, serving as a diagnostic for deployed fiber links.
A practical consequence drawn here: since E[X_min] < μ for any non-degenerate distribution, q-swap preprocessing carries a strict penalty in heterogeneous photonic networks, not just a benefit.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Request a human review

A listed scientist reviews the paper for a fee and the review publishes here regardless of verdict. See the reviewers or get listed.

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

Dear colleague,

The short take: this is a clean, honest paper that derives a formula mapping polarization-dependent loss to a singlet-conversion probability for a Bell pair and shows what SCP distributions result from three telecom PDL models. The math is correct; the application is physically motivated but the paper oversells the realism because the map assumes a specific geometry that is not stated.

What's new and good: the combined step of taking published PDL statistics and feeding them through X(P)=2/(1+10^{P/10}) via the change-of-variables in Eq. (4) is, as far as I can tell, not in the literature. The derivation is self-contained, the weak-PDL expansion to order P^3 is correct (and it's nice that the quadratic term cancels), and the three example distributions produce plausible average SCPs around 0.71–0.76. The paper is also careful to attribute the random percolation framework to the author's prior [13] and the q-swap min formula to Bose et al. [3]. No citation problems.

The main soft spot is the physical modeling. Eq. (3) follows only if PDL acts as a local filter on one qubit of the pair and the other qubit is lossless. The paper states this in Section 3 but never says that this is an assumption or discusses what happens in more realistic geometries. If both photons co-propagate through the same PDL element, the formula changes to X=2/(1+10^{P/5}); if they traverse independent PDL channels with magnitudes P1 and P2, the relevant density is the convolution of f_P with itself, not Eq. (4). Since the paper adopts single-channel telecom PDL statistics and calls the setting 'realistic quantum networks,' this ambiguity is not cosmetic: the reported mean SCPs and hence any percolation threshold estimate depend on it. A short paragraph acknowledging the geometry dependence would sharpen the claim considerably.

Two smaller points. The paper never applies the induced SCP distributions to an actual percolation threshold; it only gives the averages and stops. Given the title, that feels like an unfinished last mile. And it doesn't include the probability that the Bell pair survives the channel at all; the edge is treated as present with SCP X, whereas in practice a lossy link also has a finite occupation probability that would interact with the percolation picture. That's a minor modeling choice, but it should be flagged.

Overall, the paper deserves a serious referee: the derivation is formally sound and the connection between PDL statistics and random edge entanglement is useful for quantum-network modelers. With a few clarifying sentences about the geometry and a sensitivity check on the two-sided case, I could see it being accepted. I'd bring it to a reading group if the topic is on people's radar, and I'd cite it for the one-sided map if I needed it.

Recommendation: send it to peer review; the referee should ask for the geometry discussion and a note on the survival probability.

Referee Report

2 major / 4 minor

Summary. The paper studies random entanglement percolation in quantum networks where edge singlet-conversion probabilities (SCPs) are drawn from a distribution rather than fixed. It recalls results from the author's previous work: random classical entanglement percolation (RCEP) depends only on the mean SCP, while random quantum entanglement percolation (RQEP) depends on the full distribution through E[X_min]. The main new contribution is a physical mechanism: polarization-dependent loss (PDL) acting on a Bell pair is treated as a local filter on one qubit, leading to the closed-form map X(P)=2/(1+10^{P/10}) (Eq. 3) and the induced SCP density (Eq. 4). The paper illustrates this with three telecom PDL models (Mecozzi–Shtaif, Galtarossa–Palmieri, Lin–Jiang), reports mean SCPs, and gives a weak-PDL expansion (Eq. 5). The authors conclude that RCEP thresholds in photonic networks are set by the mean of the induced SCP distribution.

Significance. If the physical modelling assumptions are made explicit, the paper is a useful, concise contribution: it connects well-established classical fiber-optic PDL statistics to the edge-SCP distributions used in random entanglement percolation. The derivations of Eqs. (3)–(5) are transparent and mathematically correct. The use of three realistic PDL models gives the work a quantitative character and makes the predicted means readily checkable. The main caveats are not algebraic but physical: the derivation is conditional on successful photon transmission, and the assumed geometry (one photon affected by PDL) is not stated explicitly. These issues affect the quantitative percolation predictions but are addressable within the manuscript's scope.

major comments (2)

[Section 3, Eqs. (3)–(4) and reported means] The derivation conditions on successful transmission of the polarized photon(s). PDL is a loss mechanism: for a one-sided filter with intensity transmissions η1≥η2, the pair survives the channel with probability p=(η1+η2)/2 (in the simplest case). The unconditional edge SCP distribution is therefore a mixture of an atom at 0 with probability 1−p and the density (4) with weight p. Since RCEP depends on the unconditional mean E[X], the reported values μMS≈0.714, μGP≈0.739, μLJ≈0.755 are conditional means; the effective mean for percolation is p·μ_cond (modulo the exact loss model). If the network is post-selected so that every edge is present, this must be stated explicitly and the loss probability must be assigned to the edge-existence parameter of the percolation model. As written, the text conflates the conditional SCP distribution with the full edge distribution, which is load-bearing
[Section 3, Eq. (3)] The map X(P)=2/(1+10^{P/10}) assumes PDL acts on exactly one photon of the Bell pair. If both photons traverse the same PDL element, the amplitudes are filtered twice and the SCP becomes 2/(1+10^{P/5}); if the two photons traverse independent PDL elements with imbalances P1 and P2, the effective imbalance is P1+P2 and Eq. (4) must use the convolution f_P*f_P. The manuscript should specify the physical layout it has in mind (e.g., an entangled source at one node with a single photon transmitted through the PDL channel) and, ideally, discuss whether the conclusions are sensitive to this choice. Without this specification, the statement that 'any physically motivated distribution of the channel imbalance P induces a corresponding distribution of edge SCPs' overstates the generality of Eq. (4).

minor comments (4)

[Section 3] State explicitly that the density in Eq. (4) is normalized on (0,1] and represents a conditional distribution given successful transmission; the unconditional law includes an atom at zero (see major comment).
[Section 3] Define η1 and η2 as power transmissions of the two polarization modes, and note that P=10log10(η1/η2) is defined for η1≥η2. It would help to clarify whether these are intensity or amplitude transmission coefficients, since the map depends on that convention.
[Eq. (5)] The weak-PDL expansion is correct (the quadratic term cancels), but the phrasing 'can be expanded and then averaged' could be misread as requiring P to be small in distribution. The O(P^3) term is pointwise; averaging is then trivial. Please clarify.
[General] The abbreviations RCEP and RQEP are used without definition in the abstract and introduction. Define them at first use in the body.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the PDL-to-SCP map is derived from standard external results and simple calculus, with self-citations used only as background.

full rationale

The derivation chain in Section 3 is self-contained and non-circular. Equation (3) follows by substituting P = 10 log10(η1/η2) into the standard singlet-conversion formula X = 2η2/(η1+η2), which the paper explicitly attributes to external works [16,17]. Equation (4) is a direct change of variables from the PDL density f_P to the SCP density f_X, and is obtained by ordinary calculus from Eq. (3). The RCEP/RQEP formulas, Eqs. (1) and (2), are recalled from the author's previous work [13], but they are simple distributional identities used as framing; the new claim about PDL-induced SCP distributions does not reduce to them. The reported values μMS, μGP, and μLJ are evaluations of the derived map using external PDL models [18-20], not fitted parameters renamed as predictions. The skeptical concern about one-sided versus two-sided PDL geometry concerns the modeling assumptions under which Eq. (3) applies; that is a correctness risk or limitation, not a circularity in the derivation. No circular step can be exhibited, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central map is a straightforward change of variables starting from a standard PDL-filter model; no free parameters are fit to the target result. The illustrative figure uses hand-chosen PDL parameters and the random-percolation framework is inherited from [13], but the PDL-to-SCP derivation itself is self-contained.

free parameters (2)

Mean PDL ⟨P⟩ for illustration = ≈ 2.35 dB
Chosen by hand to align the Mecozzi–Shtaif and Galtarossa–Palmieri curves in Fig. 1; illustrative, not load-bearing for the map itself.
Lin–Jiang five-element PDL setting = (0.8, 1.2, 1.4, 1.0, 0.7) dB
A specific instance from reference [20] used for the third curve; illustrative.

assumptions (4)

standard math For a pure two-qubit state with Schmidt coefficients sqrt(λ1), sqrt(λ2), the singlet-conversion probability is 2 min(λ1,λ2).
Invoked in Sec. 3 to obtain X = 2η2/(η1+η2) after the PDL filter and post-selection; a standard result in entanglement theory.
domain assumption PDL acts as a local filter on one qubit of a polarization Bell state, preserving purity.
Section 3, 'PDL acts effectively as a local filter on one qubit of a polarization-entangled pair [16,17]'. This is the physical model underlying Eq. (3).
domain assumption The PDL statistics models of Mecozzi–Shtaif [18], Galtarossa–Palmieri [19], and Lin–Jiang [20] describe PDL in the relevant optical links.
Used in Sec. 3/Fig. 1 to compute representative induced SCP densities and average SCPs.
domain assumption Random classical entanglement percolation depends only on the mean SCP, and a q-swap produces SCP X_min = min(X1,X2).
Eqs. (1)-(2) are recalled from the author's prior [13] and Bose et al. [3]; the current paper does not re-derive them.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Random entanglement percolation on realistic quantum networks." pith.science (2026). https://pith.science/paper/JRWZILY5

@misc{pith2026260421967,
  author       = {Pith},
  title        = {Pith review of: Random entanglement percolation on realistic quantum networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRWZILY5}},
  note         = {Machine review of arXiv:2604.21967}
}

read the original abstract

We study random entanglement percolation in heterogeneous quantum networks, where the singlet-conversion probabilities (SCPs) of the edges are drawn from a probability distribution rather than being fixed. After briefly recalling random classical and random quantum entanglement percolation, we focus on polarization-dependent loss (PDL) as a physical source of random edge entanglement in photonic networks. In this setting, polarization imbalance induces a simple map from the PDL magnitude to the edge SCP. We illustrate this map for representative PDL models and discuss the resulting implications for entanglement percolation.

Figures

Figures reproduced from arXiv: 2604.21967 by the authors.

**Figure 1.** – Left: probability density of the polarization-dependent loss P. Right: corresponding induced SCP density obtained from Eq. (4). The Mecozzi–Shtaif and Galtarossa–Palmieri curves were matched to the same mean PDL, hPi ≈ 2.35 dB, while the Lin–Jiang model used the fiveelement setting (0.8, 1.2, 1.4, 1.0, 0.7) dB. 3. – Physically Motivated Edge Distributions In photonic quantum networks, qubits can be encoded in ort… view at source ↗

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

21 extracted references · 17 canonical work pages

[13]

Entanglement Percolation in Rando m Quantum Networks

Alessandro Romancino et al. “Entanglement Percolation in Rando m Quantum Networks”. In: Quantum Science and Technology (2026). issn: 2058-9565. doi: 10.1088/2058-9565/ae5fca

work page doi:10.1088/2058-9565/ae5fca 2026
[3]

Puriﬁcation via Entangleme nt Swapping and Conserved Entanglement

S. Bose, V. Vedral, and P. L. Knight. “Puriﬁcation via Entangleme nt Swapping and Conserved Entanglement”. In: Physical Review A 60.1 (July 1, 1999), pp. 194–197. issn: 1050-2947, 1094-1622. doi: 10.1103/PhysRevA.60.194

work page doi:10.1103/physreva.60.194 1999
[1]

Quantum internet: A vision for the road ahead

Stephanie Wehner, David Elkouss, and Ronald Hanson. “Quantum Internet: A Vision for the Road Ahead”. In: Science 362.6412 (Oct. 19, 2018), eaam9288. doi: 10.1126/science.aam9288

work page doi:10.1126/science.aam9288 2018
[2]

The Quantum Internet

H. J. Kimble. “The Quantum Internet”. In: Nature 453.7198 (June 2008), pp. 1023–

2008
[4]

Quantum Privacy Ampliﬁcation and the Secur ity of Quantum Cryptography over Noisy Channels

David Deutsch et al. “Quantum Privacy Ampliﬁcation and the Secur ity of Quantum Cryptography over Noisy Channels”. In: Physical Review Letters 77.13 (Sept. 23, 1996), pp. 2818–2821. doi: 10.1103/PhysRevLett.77.2818

work page doi:10.1103/physrevlett.77.2818 1996
[5]

Quantum Repeaters Based on Entanglement Puriﬁ cation

W. D¨ ur et al. “Quantum Repeaters Based on Entanglement Puriﬁ cation”. In: Phys- ical Review A 59.1 (Jan. 1, 1999), pp. 169–181. issn: 1050-2947, 1094-1622. doi: 10.1103/PhysRevA.59.169

work page doi:10.1103/physreva.59.169 1999
[6]

Entang lement Percolation in Quantum Networks

Antonio Ac ´ ın, J. Ignacio Cirac, and Maciej Lewenstein. “Entang lement Percolation in Quantum Networks”. In: Nature Physics 3.4 (Apr. 2007), pp. 256–259. issn: 1745-2481. doi: 10.1038/nphys549

work page doi:10.1038/nphys549 2007
[7]

Distribution of Entanglement in Large-Scale Quantum Net- works

S Perseguers et al. “Distribution of Entanglement in Large-Scale Quantum Net- works”. In: Reports on Progress in Physics 76.9 (Sept. 2013), p. 096001. issn: 0034-4885. doi: 10.1088/0034-4885/76/9/096001

work page doi:10.1088/0034-4885/76/9/096001 2013

Show all 21 references

[8]

Deterministic Entanglement Distribution on Se ries-Parallel Quantum Networks

Xiangyi Meng et al. “Deterministic Entanglement Distribution on Se ries-Parallel Quantum Networks”. In: Physical Review Research 5.1 (Mar. 31, 2023), p. 013225. issn: 2643-1564. doi: 10.1103/PhysRevResearch.5.013225. RANDOM ENTANGLEMENT PERCOLATION ON REALISTIC QUANTUM NETW ORKS 5

2023 doi
[9]

Complex Qu antum Net- works: A Topical Review

Johannes Nokkala, Jyrki Piilo, and Ginestra Bianconi. “Complex Qu antum Net- works: A Topical Review”. In: Journal of Physics A: Mathematical and Theoretical 57.23 (May 2024), p. 233001. issn: 1751-8121. doi: 10.1088/1751-8121/ad41a6

2024 doi
[10]

Entanglement Percolation in Quantum Com- plex Networks

Mart ´ ı Cuquet and John Calsamiglia. “Entanglement Percolation in Quantum Com- plex Networks”. In: Physical Review Letters 103.24 (Dec. 10, 2009), p. 240503. doi: 10.1103/PhysRevLett.103.240503

2009 doi
[11]

Quantum Communication Networks Enhance d by Distributed Quantum Memories

Xiangyi Meng et al. “Quantum Communication Networks Enhance d by Distributed Quantum Memories”. In: Quantum 9 (Dec. 15, 2025), p. 1948. issn: 2521-327X. doi: 10.22331/q-2025-12-15-1948

2025 doi
[12]

Dynamical Entanglement Percolation wit h Spatially Cor- related Disorder

Lorenzo Cirigliano et al. “Dynamical Entanglement Percolation wit h Spatially Cor- related Disorder”. In: arXiv preprint (Jan. 9, 2026). doi: 10.48550/arXiv.2601.05925. arXiv: 2601.05925 [quant-ph] . Pre-published

2026 doi
[14]

Passively Stable Distribution of Pola risation Entangle- ment over 192 Km of Deployed Optical Fibre

S¨ oren Wengerowsky et al. “Passively Stable Distribution of Pola risation Entangle- ment over 192 Km of Deployed Optical Fibre”. In: npj Quantum Information 6.1 (Jan. 10, 2020), p. 5. issn: 2056-6387. doi: 10.1038/s41534-019-0238-8

2020 doi
[15]

Demonstration of Quantum Network Pr otocols over a 14- Km Urban Fiber Link

Stephan Kucera et al. “Demonstration of Quantum Network Pr otocols over a 14- Km Urban Fiber Link”. In: npj Quantum Information 10.1 (Sept. 14, 2024), p. 88. issn: 2056-6387. doi: 10.1038/s41534-024-00886-x

2024 doi
[16]

Tuning Q uantum Channels to Maximize Polarization Entanglement for Telecom Photon Pairs

Daniel E. Jones, Brian T. Kirby, and Michael Brodsky. “Tuning Q uantum Channels to Maximize Polarization Entanglement for Telecom Photon Pairs”. In : npj Quan- tum Information 4.1 (Nov. 6, 2018), p. 58. issn: 2056-6387. doi: 10.1038/s41534-018-0107-x

2018 doi
[17]

Eﬀect o f Polarization Dependent Loss on the Quality of Transmitted Polarization Entangle ment

Brian T. Kirby, Daniel E. Jones, and Michael Brodsky. “Eﬀect o f Polarization Dependent Loss on the Quality of Transmitted Polarization Entangle ment”. In: Journal of Lightwave Technology 37.1 (Jan. 2019), pp. 95–102. issn: 1558-2213. doi: 10.1109/JLT.2018.2879754

2019
[18]

The Statistics of Polarization-Depe ndent Loss in Opti- cal Communication Systems

A. Mecozzi and M. Shtaif. “The Statistics of Polarization-Depe ndent Loss in Opti- cal Communication Systems”. In: IEEE Photonics Technology Letters 14.3 (Mar. 2002), pp. 313–315. issn: 1941-0174. doi: 10.1109/68.986797

2002 doi
[19]

The Exact Statistics of Polarizat ion-Dependent Loss in Fiber-Optic Links

A. Galtarossa and L. Palmieri. “The Exact Statistics of Polarizat ion-Dependent Loss in Fiber-Optic Links”. In: IEEE Photonics Technology Letters 15.1 (Jan. 2003), pp. 57–59. issn: 1941-0174. doi: 10.1109/LPT.2002.805799

2003
[20]

Generalized Probability Density Funct ion of Polarization- Dependent Loss in Optical Links

Xiang Lin and Zhiping Jiang. “Generalized Probability Density Funct ion of Polarization- Dependent Loss in Optical Links”. In: IEEE Photonics Technology Letters 36.2 (Jan. 2024), pp. 79–82. issn: 1941-0174. doi: 10.1109/LPT.2023.3336211

2024
[1030]

doi: 10.1038/nature07127

issn: 1476-4687. doi: 10.1038/nature07127

doi

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [13]

Entanglement Percolation in Rando m Quantum Networks

Alessandro Romancino et al. “Entanglement Percolation in Rando m Quantum Networks”. In: Quantum Science and Technology (2026). issn: 2058-9565. doi: 10.1088/2058-9565/ae5fca

work page doi:10.1088/2058-9565/ae5fca 2026

[2] [3]

Puriﬁcation via Entangleme nt Swapping and Conserved Entanglement

S. Bose, V. Vedral, and P. L. Knight. “Puriﬁcation via Entangleme nt Swapping and Conserved Entanglement”. In: Physical Review A 60.1 (July 1, 1999), pp. 194–197. issn: 1050-2947, 1094-1622. doi: 10.1103/PhysRevA.60.194

work page doi:10.1103/physreva.60.194 1999

[3] [1]

Quantum internet: A vision for the road ahead

Stephanie Wehner, David Elkouss, and Ronald Hanson. “Quantum Internet: A Vision for the Road Ahead”. In: Science 362.6412 (Oct. 19, 2018), eaam9288. doi: 10.1126/science.aam9288

work page doi:10.1126/science.aam9288 2018

[4] [2]

The Quantum Internet

H. J. Kimble. “The Quantum Internet”. In: Nature 453.7198 (June 2008), pp. 1023–

2008

[5] [4]

Quantum Privacy Ampliﬁcation and the Secur ity of Quantum Cryptography over Noisy Channels

David Deutsch et al. “Quantum Privacy Ampliﬁcation and the Secur ity of Quantum Cryptography over Noisy Channels”. In: Physical Review Letters 77.13 (Sept. 23, 1996), pp. 2818–2821. doi: 10.1103/PhysRevLett.77.2818

work page doi:10.1103/physrevlett.77.2818 1996

[6] [5]

Quantum Repeaters Based on Entanglement Puriﬁ cation

W. D¨ ur et al. “Quantum Repeaters Based on Entanglement Puriﬁ cation”. In: Phys- ical Review A 59.1 (Jan. 1, 1999), pp. 169–181. issn: 1050-2947, 1094-1622. doi: 10.1103/PhysRevA.59.169

work page doi:10.1103/physreva.59.169 1999

[7] [6]

Entang lement Percolation in Quantum Networks

Antonio Ac ´ ın, J. Ignacio Cirac, and Maciej Lewenstein. “Entang lement Percolation in Quantum Networks”. In: Nature Physics 3.4 (Apr. 2007), pp. 256–259. issn: 1745-2481. doi: 10.1038/nphys549

work page doi:10.1038/nphys549 2007

[8] [7]

Distribution of Entanglement in Large-Scale Quantum Net- works

S Perseguers et al. “Distribution of Entanglement in Large-Scale Quantum Net- works”. In: Reports on Progress in Physics 76.9 (Sept. 2013), p. 096001. issn: 0034-4885. doi: 10.1088/0034-4885/76/9/096001

work page doi:10.1088/0034-4885/76/9/096001 2013