Continuous-Variable Multiplexed Quantum Repeater Networks

Kae Nemoto; Nicol\'o Lo Piparo; Pei-Zhe Li; William J. Munro

REVIEW 3 major objections 4 minor 68 references

Continuous-Variable Multiplexed Quantum Repeater Networks

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Multiplexing cat-code repeaters with a few extra channels lifts the secret key rate from 10^-14 to 10^-3 bits per channel.

desk verdict Memory-based multiplexing is the real result; graph-state claims need a general-m proof before they're cited. read the letter →

arxiv 2411.14757 v1 pith:SJL5MZYC submitted 2024-11-22 quant-ph

Pei-Zhe Li , William J. Munro , Kae Nemoto , Nicoló Lo Piparo This is my paper · ORCID

classification quant-ph MSC 81P4581P94 PACS 03.67.Hk03.67.Dd

keywords QuantumrepeatersCatcodesContinuous-variablekeydistributionSecretrateMultiplexingmemoriesGraphstatesRotation-symmetricbosonic

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

Continuous-variable quantum repeaters based on cat codes—bosonic codes whose codewords are superpositions of coherent states—have been experimentally feasible but suffered from secret key rates too low for practical use. This paper claims that the low rate comes from using a single channel and averaging over all syndrome outcomes, and that multiplexing with a few parallel copies of the encoded state fixes the problem. With $m=3$ channels, the secret key rate for 1-loss cat codes rises from roughly $10^{-14}$ to $10^{-3}$ bits per channel, and the protocol becomes comparable to third-generation discrete-variable repeaters while using far fewer optical resources. The paper also presents a graph-state version that avoids quantum memories entirely, at the price of sensitivity to measurement errors, and it identifies a concrete trade-off between memory coherence time and measurement error.

What carries the argument

The load-bearing construction is the multiplexed elementary link: $m$ identical cat-coded light modes travel in parallel between ES1 and ES2 stations, and at each ES2 a syndrome measurement on ancillary qubits selects the desired photon-loss outcome. In the memory-based variant, matter qubits at ES1 wait in quantum memories until classical communication identifies successful channels, giving repetition time $t_{r,2}=\max\{t_0,2L_0/c\}$. In the graph-state variant, each ES1 holds a continuous-variable graph state whose nodes are cat-coded modes; measuring failed nodes in the logical $Z$ basis removes them and leaves a Bell pair among the survivors, so no memory and no waiting time are needed and $t_{r,3}=t_0$. The mathematical core is the Appendix B fidelity analysis: after syndrome selection and node removal, the surviving state is equivalent to the no-loss transmitted state, giving the graph-state secret key rate $R_{\rm QKD,3}=[1-(1-P_{\rm dsm})^m]^n(P_{\rm USD}p_m)^{mn}[1-h(1-F_{\rm tot,3})]/t_0$, with $k_m=mn$ logical $Z$ measurements counted for graph states and $k_m=n$ for the quantum-memory version.

What would settle it

Directly compute the graph-state protocol for $m=3$ channels: construct the three-channel graph state, apply the amplitude-damping loss channel to every mode, project onto the desired syndrome outcomes, discard the failed nodes, and check whether the surviving two-mode state has fidelity equal to the no-loss case; at the same time, re-derive Eq. (6) by counting all logical $Z$ measurements in the network, since each ES2 connects nodes from two ES1s and the count could be $2mn$ rather than $nm$.

Watch

Extended reading notes

Core claim

The central claim is that the poor performance of cat-code repeaters is not intrinsic to the cat code but a consequence of single-channel operation, which forces a compromise value of the mean photon number $\alpha$ across different loss outcomes. By sending $m$ identical cat-coded light modes in parallel between elementary stations and selecting only channels whose syndrome measurement gives the desired even (or odd) photon-loss number, the paper obtains a large success-probability boost and can fix $\alpha$ at its optimal value. For the memory-based version, quantum memories at the ES1 stations hold matter qubits until classical communication announces which channels succeeded; decoherence is modeled by depolarizing or dephasing channels. For the memory-free version, a continuous-variable graph state whose nodes are cat-coded modes is created through cavity-QED light-matter interactions; after nodes with undesired syndrome outcomes are removed by logical $Z$ measurements, the remaining state is claimed to be a Bell pair with fidelity equal to the no-loss case. With 3-loss cat codes and $0.1\%$ measurement error, the paper reports secret key rates around $2\times10^5$ bits/s at 100 km and $7\times10^3$ bits/s at 1000 km, comparable to a third-generation discrete-variable repeater that encodes in hundreds of photons.

Load-bearing premise

The whole graph-state result rests on the unproven-in-general assumption that the same 'remove bad nodes and get a perfect Bell pair' trick works for any number of parallel channels; the paper demonstrates this explicitly only for two channels, and its counting of the number of repeated measurements may be off by a factor of two.

Editorial extensions

If this is right

For 1-loss cat codes, multiplexing with $m=3$ channels raises the secret key rate from about $10^{-14}$ to $10^{-3}$ bits per channel at $\alpha\approx1.268$, more than ten orders of magnitude, using only a few extra channels.
The graph-state version eliminates quantum memories and the associated waiting time, setting the repetition time to $t_0$ rather than $\max\{t_0,2L_0/c\}$, and, under the Appendix B argument, still yields a Bell pair with the no-loss fidelity.
With 3-loss cat codes and $0.1\%$ measurement error, the protocol reaches about $2\times10^5$ bits/s at 100 km and $7\times10^3$ bits/s at 1000 km, comparable to a third-generation discrete-variable repeater that requires hundreds of photons.
For a fixed secret key rate, the protocol tolerates quantum-memory coherence times around one minute under depolarizing noise and roughly three orders of magnitude smaller under dephasing noise, trading off against gate measurement error.
At a fixed cost coefficient $C'=100$, the multi-channel cat-code repeater permits longer elementary distances than the binomial-code single-channel repeater, reducing the number of stations and auxiliary devices along a 1000 km link.

Reading between the lines

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

If the Appendix B fidelity equality holds for all $m$, the graph-state protocol becomes a memory-free multiplexed repeater whose rate benefits directly from more parallel channels; a comparison with other multiplexed continuous-variable schemes at fixed total photon number would show where the advantage saturates.
The paper's counting of logical $Z$ measurements in the graph-state rate, $k_m=nm$, may undercount: each ES2 receives nodes from two ES1s, so the number could be $2mn$; if so the plotted graph-state secret key rate would fall by a factor $(P_{\rm USD}p_m)^{mn}$, which would shrink but not necessarily erase the multiplexing gain for small $m$.
The assumption that at least one channel per elementary link succeeds, $[1-(1-P_{\rm dsm})^m]^n$, implicitly assumes independent channels and no correlated losses; a natural extension is to test whether realistic fiber correlations or detector dark counts change the optimal $m$ and $\alpha$.
Since the authors note that local losses accumulate at every elementary station, adding a local-loss term to $F_{\rm tot}$ for both variants and recomputing the Figure 5 crossing points would show how the graph-state advantage degrades when local errors dominate.

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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

Quick take: the result that actually carries the paper is the memory-based multiplexing. That part looks right to me, and it is enough to justify the headline order-of-magnitude improvement (Fig. 4). The graph-state variant is the fragile piece: its central claim—that after syndrome selection and removal of undesired nodes the final state is a Bell pair with no-loss fidelity—is proven only for m=2 in Appendix B, then used for arbitrary m in Eq. (11). That's a gap, not a contradiction, so I'd send it to a serious referee but ask for a general proof or a worked example for m=3.

On the counting worry: I think that's a misread. In the m=2 example, the four-mode graph belongs to one ES1 and spans two elementary links—two nodes travel left, two travel right. Each of the four nodes is measured once in logical Z (two removals, two entanglement-creation measurements), so four measurements per two links, i.e. km = nm. The exponent in Eq. (6) is correct as written.

What's new: applying multiplexing to CV cat-code repeaters, using QMs or graph states to pick a favorable syndrome outcome; the cavity-QED construction of photonic graph states with RSBC nodes (Appendix A); and the resource comparison with third-generation DV repeaters. The memory analysis with dephasing and depolarizing noise is standard but applied cleanly, and the trade-off between memory coherence time and measurement error in Fig. 5 is a useful plot.

Soft spots, in proportion: the unproved m-to-general fidelity equivalence is the main one. The comparison with [40] is narrow—one error probability, one code family—so the claim of "comparable performance" rests on a single point. There are also typos (Eq. B6 repeats the |1bar> line; "to to" in the conclusions) and the graph-state SKR in Eq. (11) should be treated as provisional until the fidelity argument is filled in. None of this undermines the QM result, which stands on its own.

Who this is for: anyone working on CV repeaters or memory-based long-distance QKD. The graph-state construction in Appendix A is the most original part, even if its performance claim needs work. I'd referee it, with the fidelity generalization as a mandatory revision.

Referee Report

3 major / 4 minor

Summary. The paper proposes two multiplexed continuous-variable quantum repeater protocols based on cat codes: one using a few quantum memories at the elementary stations, and one replacing those memories with graph states whose nodes are logical cat-code states. For each protocol, the authors derive a secret-key-rate formula (Eqs. 10 and 11), including the probability of desired syndrome outcomes, the success probability of the logical-Z unambiguous state discrimination, and, for the memory-based protocol, the effect of finite coherence time modeled as dephasing or depolarizing noise. The central claimed results are that a small number of channels per elementary link (m=2,3,4) raises the SKR by many orders of magnitude relative to the single-channel cat-code repeater, that the graph-state version can reach the same fidelity as the no-loss case while removing the need for quantum memories, and that the 3-loss cat-code implementation becomes competitive with a third-generation discrete-variable repeater while using fewer optical resources.

Significance. If the claims are correct, the paper is significant: it would show that cat-code repeaters, which are experimentally accessible at optical frequencies without frequency conversion, can reach performance comparable to leading DV repeater proposals with far fewer resources. The paper contains explicit analytical derivations of graph-state generation and of the m=2 fidelity equivalence, and the SKR formulas are derived from the protocol assumptions and standard QKD secret-fraction expressions rather than fitted to the claimed improvement. The main quantitative claims are, however, sensitive to two points that are not fully established: the fidelity equivalence for the graph-state protocol is proven only for a special m=2 case, and the counting of logical-Z measurements that enters Eq. (11) is stated in a way that is easy to misread. Both issues are fixable, but they are load-bearing for the graph-state protocol's performance claims.

major comments (3)

[Appendix B / Eq. (11)] The fidelity equivalence that underlies F_tot,3 in Eq. (11) is demonstrated only for the special case m=2, and only for the post-selection pattern in which exactly one node on each side of the graph has the desired even-loss syndrome (modes 1 and 4) and exactly one node on each side has odd loss (modes 2 and 3). The protocol as described in Section II.B accepts any outcome with at least one desired syndrome per side, and Eq. (4) sums over all such events; cases with multiple desired nodes per side or with m>2 are not analyzed, and the graph state for general m is not specified. Because Eq. (11) and Figures 5 and 7 use F_tot,3 for optimized values of m, the graph-state secret-key rates and the comparison with Ref. [40] rest on an unproven generalization. Please provide a derivation for general m or state and justify this as an assumption.
[Section II.C, Eq. (6), and Appendix B] The counting km=nm for the graph-state protocol is internally consistent only if n is the number of directed ES1-to-ES2 elementary links, so that the four-mode graph in Appendix B represents one ES1 with two incident elementary links (left and right), each carrying m=2 channels, and hence 2m=4 logical-Z measurements in total. The text defines n=Ltot/L0 as "the number of elementary links" but does not specify whether an elementary link is a directed ES1-ES2 segment or an ES2-ES2 connection; under the latter reading, each ES2 receives m nodes from each adjacent ES1 and the exponent in Eq. (6) would be 2mn, not mn. Because Eq. (11) is exponentially sensitive to this exponent, the definition must be made explicit.
[Eq. (11) and Figures 5/7] The manuscript never states the explicit expression for F_tot,3 used in the numerical evaluation of Eq. (11). Appendix B proves only a single-link fidelity equivalence for m=2; the multi-link total fidelity after n entanglement swaps, the values of F0, Pdsm, eta, t0, and the optimized m and alpha used in Figures 5 and 7 are not given. Without these, the graph-state curves and the claimed comparison with the third-generation repeater of Ref. [40] are not reproducible. Please include the full parameter table and the formula for F_tot,3.

minor comments (4)

[Appendix B, Eq. (B6)] In Eq. (B6), the action of A_{2m+1} on |bar{1}> is listed twice; the second line should act on |bar{0}> and yield |tilde{0}_->, matching the relations stated immediately after Eq. (B9).
[Throughout] There are numerous typos, including "Eqation" near Eqs. (B15)-(B16), "normaliza=on constant" after Eq. (B11), "to to" in Section IV, and "sold" for "solid" in the Figure 7 caption; these should be corrected.
[Figures 4 and 5] The captions should state which protocol (QMs or graph states) is plotted, whether pm=1 in Figure 4, and the optimized values of m and alpha used in Figure 5; currently the text refers to these only indirectly.
[Section II.C, Eq. (4)] The phrase "at least one syndrome measurement will give the desired outcome" in the derivation of Eq. (4) should be "at least one channel in each elementary link", since the probability is for a per-link event.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the multiplexed-SKR claims follow from the paper's own protocol combinatorics together with single-channel physical inputs from published prior work, with no equation equal to its own input by construction.

full rationale

The derivation chain for the central claims is not circular. Eqs. (10)-(11) assemble three ingredients: the multiplexing factor P_tdsm = [1-(1-P_dsm)^m]^n (Eq. 4), which is this paper's own combinatorics for selecting at least one desired syndrome outcome per elementary link; the unambiguous-state-discrimination factor P_tz = (P_USD p_m)^(km) (Eq. 6), with P_USD from the external Dieks/Peres bound (Eq. 5) and km counted from the protocol; and the standard secret-fraction expression r_inf = 1 - h(e_x) - h(e_z) (Eq. 9). The headline improvement from ~10^-14 to ~10^-3 bits/ch (Fig. 4) is visible in the closed-form ratio [1-(1-P_dsm)^m]^n / P_dsm^n, and no parameter is fitted to force that number: alpha and m are optimized free parameters, while P_dsm is the single-channel syndrome-outcome probability taken from the peer-reviewed prior analyses [46,47]. Those prior citations are real evidence under the reviewing rules - they are parameter-free computations (given alpha, eta, and the cat-code codewords) with stated physical assumptions that do not include the multiplexed SKR or the graph-state fidelity - so their author overlap does not constitute load-bearing circularity. The graph-state fidelity claim is likewise derived, not assumed: Appendix B explicitly computes, for the four-node m=2 case, that after removing undesired nodes the odd-loss coefficients factor into a global normalization (Eqs. B13-B14, B22-B24), yielding F = (Sum_even C_i)^2/(Sum C_i)^2, with the equality to transmitting |00>+|11> through the channel obtained by calculation rather than by definition. The paper does leave gaps that are correctly flagged as correctness risks: the fidelity equivalence is shown only for m=2 yet used in Eq. (11) for arbitrary m, Eq. (6) asserts km = nm for graph states without a full accounting of logical-Z measurements in the concatenated network (the m=2 example involves four such measurements), and the Concluding Discussion itself acknowledges that local losses accumulate and degrade the SKR. These are support/completeness concerns, not circular reductions: no equation in the paper is equal to its own input by construction, and no fitted quantity is renamed as a prediction.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central SKR estimates rest on standard QKD security formulas and prior cat-code results; the main resource additions are the multiplexing order m and memory/measurement quality parameters, all treated as tunable inputs rather than fitted outputs.

free parameters (5)

alpha (mean photon number of cat code) = optimized around 1.268 for 1-loss codes; other values for 3-loss codes
Chosen to maximize SKR; multiplexing allows selecting a favorable alpha instead of trading off among syndrome outcomes.
m (number of channels per link) = varied from 2 to 4 in Figure 4
Resource knob optimized for SKR; central to the multiplexing advantage.
pm (measurement error probability) = 1-pm = 0.1% in Figure 7; threshold values in Figure 5
Assumed device parameter for logical Z discrimination; central to trade-off curves.
tc (quantum memory coherence time) = 0.05 s, 0.5 s, 5 s, 50 s
Assumed values spanning cavity-QED demonstrations; used to model QM decoherence.
L0 (elementary link length) = varied up to about 1.2 km in Figure 6
Chosen to reach a fixed cost coefficient C'=100 for protocol comparison.

assumptions (6)

domain assumption Cat-code codewords and their Kraus evolution under amplitude damping as given in [46,47]
The entire SKR and fidelity analysis uses these prior results as input; not rederived here.
standard math USD optimal success probability P_USD = 1 - |<0bar|1bar>|
Used in Eq (5) for logical Z measurement success; standard result from Dieks and Peres [61,62].
standard math Secret fraction r_inf = 1 - h(ez) - h(ex)
Standard BBM92 security analysis [60]; no finite-size or composable security terms included.
ad hoc to paper Fidelity equivalence for graph states proven for m=2 extends to arbitrary m
Appendix B derives the two-channel case; the paper asserts the generalization without proof.
domain assumption Local losses at repeater stations are neglected
Explicitly stated as a limitation in the concluding discussion; affects absolute SKR but not the relative comparison.
domain assumption Quantum memory decoherence is either pure dephasing or pure depolarizing with p=exp(-t/tc)
Used in Appendix C to model QM errors; standard but a simplification.

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Cite this review

Pith. "Pith review of Continuous-Variable Multiplexed Quantum Repeater Networks." pith.science (2026). https://pith.science/paper/SJL5MZYC

@misc{pith2026241114757,
  author       = {Pith},
  title        = {Pith review of: Continuous-Variable Multiplexed Quantum Repeater Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SJL5MZYC}},
  note         = {Machine review of arXiv:2411.14757}
}

read the original abstract

Continuous-variable (CV) codes and their application in quantum communication have attracted increasing attention. In particular, one typical CV codes, cat-codes, has already been experimentally created using trapped atoms in cavities with relatively high fidelities. However, when these codes are used in a repeater protocol, the secret key rate (SKR) that can be extracted between two remote users is extremely low. Here we propose a quantum repeater protocol based on cat codes with a few quantum memories or graph states as additional resources. This allows us to considerably increase the secret key rate by several orders of magnitude. Our findings provide valuable insights for designing efficient quantum repeater systems, advancing the feasibility and performance of quantum communication over long distances.

Figures

Figures reproduced from arXiv: 2411.14757 by the authors.

**Figure 2.** FIG. 2. The total success probability for the 1-loss cat [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Creation of graph states. The matter qubits (blue [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: FIG. 5. The measurement error probability [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. The elementary distance versus the total distance [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. The optimized SKRs of 3-loss cat codes for both [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: FIG. 8. The measurement on [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

68 extracted references · 37 canonical work pages

[40]

W. J. Munro, A. M. Stephens, S. J. Devitt, K. A. Harri- son, and K. Nemoto, Quantum communication without the necessity of quantum memories, Nature Photonics6, 777 (2012)

2012
[1]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Long- distance quantum communication with atomic ensembles and linear optics, Nature414, 413 (2001). 13

work page 2001
[2]

If the outcome is not|˜0+˜0+⟩, the final atomic state will be the state in Equation B20 with Pauli-Z op- eration(s) on corresponding matter qubit(s)

If nec- essary, we can get one of the Bell states(|↑↑⟩ + |↓↓⟩)/ √ 2 by performing a Hadamard operation on one of the mat- ter qubits. If the outcome is not|˜0+˜0+⟩, the final atomic state will be the state in Equation B20 with Pauli-Z op- eration(s) on corresponding matter qubit(s). Similarly, for | ˜ϕ+⟩2, | ˜ϕ+⟩3 and | ˜ϕ+⟩4, we have 1√ 2 (|↑⟩ + |↓⟩) | ˜...

work page
[3]

Muralidharan, J

S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, Ultrafast and fault-tolerant quantum com- munication across long distances, Phys. Rev. Lett.112, 250501 (2014)

work page 2014
[4]

Jiang, J

L. Jiang, J. M. Taylor, and M. D. Lukin, Fast and robust approach to long-distance quantum communication with atomic ensembles, Phys. Rev. A76, 012301 (2007)

2007
[5]

A. S. Cacciapuoti, M. Caleffi, F. Tafuri, F. S. Cataliotti, S. Gherardini, and G. Bianchi, Quantum internet: Net- working challenges in distributed quantum computing, IEEE Network 34, 137 (2020)

work page 2020
[6]

H. J. Kimble, The quantum internet, Nature453, 1023 (2008)

2008
[7]

A. K. Ekert, Quantum cryptography based on bell’s the- orem, Phys. Rev. Lett.67, 661 (1991)

1991

Show all 68 references

[8]

C. H. Bennett and G. Brassard, Quantum cryptogra- phy: Publickeydistributionandcointossing(IEEE,New York, 1984)

1984
[9]

T.-Y. Chen, H. Liang, Y. Liu, W.-Q. Cai, L. Ju, W.-Y. Liu, J. Wang, H. Yin, K. Chen, Z.-B. Chen, C.-Z. Peng, and J.-W. Pan, Field test of a practical secure communi- cation network with decoy-state quantum cryptography, Opt. Express 17, 6540 (2009)

2009
[10]

C.H.Bennett, G.Brassard,andN.D.Mermin,Quantum cryptography without bell’s theorem, Phys. Rev. Lett. 68, 557 (1992)

1992
[11]

Z. Qi, Y. Li, Y. Huang, J. Feng, Y. Zheng, and X. Chen, A 15-user quantum secure direct communication net- work, Light: Science & Applications10, 183 (2021)

2021
[12]

Wehner, D

S. Wehner, D. Elkouss, and R. Hanson, Quantum inter- net: A vision for the road ahead, Science362, eaam9288 (2018)

2018
[13]

P. T. Cochrane, G. J. Milburn, and W. J. Munro, Macro- scopically distinct quantum-superposition states as a bosonic code for amplitude damping, Phys. Rev. A59, 2631 (1999)

1999
[14]

I. L. Chuang, D. W. Leung, and Y. Yamamoto, Bosonic quantum codes for amplitude damping, Phys. Rev. A56, 1114 (1997)

1997
[15]

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, Hybrid quantum repeater based on dis- persive CQED interactions between matter qubits and bright coherent light, New Journal of Physics 8, 184 (2006)

2006
[16]

van Loock, T

P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, Hybrid quantum repeater using bright coherent light, Phys. Rev. Lett. 96, 240501 (2006)

2006
[17]

N.Sangouard, C.Simon, H.deRiedmatten,andN.Gisin, Quantum repeaters based on atomic ensembles and linear optics, Rev. Mod. Phys.83, 33 (2011)

2011
[18]

W. J. Munro, R. Van Meter, S. G. R. Louis, and K. Nemoto, High-bandwidth hybrid quantum repeater, Phys. Rev. Lett.101, 040502 (2008)

2008
[19]

W. J. Munro, K. Azuma, K. Tamaki, and K. Nemoto, In- side quantum repeaters, IEEE Journal of Selected Topics in Quantum Electronics21, 78 (2015)

2015
[20]

Van Meter, Quantum networking (John Wiley & Sons, Ltd, 2014)

R. Van Meter, Quantum networking (John Wiley & Sons, Ltd, 2014)

2014
[21]

Nemoto, M

K. Nemoto, M. Trupke, S. J. Devitt, B. Scharfenberger, K. Buczak, J. Schmiedmayer, and W. J. Munro, Pho- tonic quantum networks formed from NV-centers, Scien- tific Reports 6, 26284 (2016)

2016
[22]

Azuma, K

K. Azuma, K. Tamaki, and H.-K. Lo, All-photonic quan- tum repeaters, Nature Communications6, 6787 (2015)

2015
[23]

Deutsch, A

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, Quantum privacy ampli- fication and the security of quantum cryptography over noisy channels, Phys. Rev. Lett.77, 2818 (1996)

1996
[24]

Azuma, S

K. Azuma, S. E. Economou, D. Elkouss, P. Hilaire, L. Jiang, H.-K. Lo, and I. Tzitrin, Quantum repeaters: From quantum networks to the quantum internet, Rev. Mod. Phys. 95, 045006 (2023)

2023
[25]

W.Dür, H.-J.Briegel, J.I.Cirac,andP.Zoller,Quantum repeaters based on entanglement purification, Phys. Rev. A 59, 169 (1999)

1999
[26]

Briegel, W

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quan- tum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett.81, 5932 (1998)

1998
[27]

Muralidharan, C.-L

S. Muralidharan, C.-L. Zou, L. Li, J. Wen, and L. Jiang, Overcoming erasure errors with multilevel systems, New Journal of Physics19, 013026 (2017)

2017
[28]

Jiang, J

L. Jiang, J. M. Taylor, K. Nemoto, W. J. Munro, R. Van Meter, and M. D. Lukin, Quantum repeater with encoding, Phys. Rev. A79, 032325 (2009)

2009
[29]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, Experimental demonstration of four-photon entanglement and high-fidelity teleportation, Phys. Rev. Lett. 86, 4435 (2001)

2001
[30]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy chan- nels, Phys. Rev. Lett.76, 722 (1996)

1996
[31]

Simon and J.-W

C. Simon and J.-W. Pan, Polarization entanglement pu- rification using spatial entanglement, Phys. Rev. Lett. 89, 257901 (2002)

2002
[32]

J.-W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zeilinger, Experimental entanglement purification of arbitrary unknown states, Nature423, 417 (2003)

2003
[33]

Reichle, D

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Experimental purification of two- atom entanglement, Nature443, 838 (2006)

2006
[34]

Maruyama and F

K. Maruyama and F. Nori, Entanglement purification without controlled-not gates by using the natural dynam- ics of spin chains, Phys. Rev. A78, 022312 (2008)

2008
[35]

C.Wang, Y.Zhang,andG.-s.Jin,Entanglementpurifica- tion and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities, Phys. Rev. A 84, 032307 (2011)

2011
[36]

Sheng, F.-G

Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, Efficient polarization-entanglement purification based on para- metric down-conversion sources with cross-kerr nonlin- earity, Phys. Rev. A77, 042308 (2008)

2008
[37]

A. G. Fowler, D. S. Wang, C. D. Hill, T. D. Ladd, R. Van Meter, and L. C. L. Hollenberg, Surface code quantum communication, Phys. Rev. Lett.104, 180503 (2010)

2010
[38]

Wang and C

T.-J. Wang and C. Wang, High-efficient entanglement distillation from photon loss and decoherence, Opt. Ex- press 23, 31550 (2015)

2015
[39]

Muralidharan, L

S. Muralidharan, L. Li, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, Optimal architectures for long 14 distance quantum communication, Scientific Reports6, 20463 (2016)

2016
[41]

Glancy, H

S. Glancy, H. M. Vasconcelos, and T. C. Ralph, Trans- mission of optical coherent-state qubits, Phys. Rev. A70, 022317 (2004)

2004
[42]

Borregaard, H

J. Borregaard, H. Pichler, T. Schröder, M. D. Lukin, P. Lodahl, and A. S. Sørensen, One-way quantum re- peater based on near-deterministic photon-emitter inter- faces, Phys. Rev. X10, 021071 (2020)

2020
[43]

Furrer and W

F. Furrer and W. J. Munro, Repeaters for continuous- variable quantum communication, Phys. Rev. A 98, 032335 (2018)

2018
[44]

Dias and T

J. Dias and T. C. Ralph, Quantum repeaters us- ing continuous-variable teleportation, Phys. Rev. A95, 022312 (2017)

2017
[45]

A. L. Grimsmo, J. Combes, and B. Q. Baragiola, Quan- tum computing with rotation-symmetric bosonic codes, Physical Review X10, 011058 (2020)

2020
[46]

K. P. Seshadreesan, H. Krovi, and S. Guha, Continuous- variable quantum repeater based on quantum scissors and mode multiplexing, Phys. Rev. Res. 2, 013310 (2020)

2020
[47]

𝐸𝑆" 𝐵𝑆𝑀𝐵𝑆𝑀Classical SignalClassical SignalClassical Signal (b) 𝐸𝑆! 𝐸𝑆! 𝐸𝑆

when cat codes are in use. We then propose a solu- tion to increase the performance of the quantum repeater arXiv:2411.14757v1 [quant-ph] 22 Nov 2024 2 by slightly modifying this system adding a few QMs at each repeater station and classical communication be- tween two adjacen...

2024 arXiv
[48]

Li and P

P.-Z. Li and P. van Loock, Memoryless quantum re- peaters based on cavity-QED and coherent states, Ad- vanced Quantum Technologies6, 2200151 (2023)

2023
[49]

P.-Z. Li, J. Dias, W. J. Munro, P. van Loock, K. Nemoto, and N. Lo Piparo, Performance of rotation-symmetric bosonic codes in a quantum repeater network, Advanced Quantum Technologies7, 2300252 (2024)

2024
[50]

L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. P. Song, C.-L. Zou, S. M. Girvin, L.-M. Duan, and L. Sun, Quantum error correction and univer- sal gate set operation on a binomial bosonic logical qubit, Nature Physics 15, 503 (2019)

2019
[51]

Z. Ni, S. Li, X. Deng, Y. Cai, L. Zhang, W. Wang, Z.- B. Yang, H. Yu, F. Yan, S. Liu, C.-L. Zou, L. Sun, S.- B. Zheng, Y. Xu, and D. Yu, Beating the break-even point with a discrete-variable-encoded logical qubit, Na- ture 616, 56 (2023)

2023
[52]

Lo Franco, G

R. Lo Franco, G. Compagno, A. Messina, and A. Napoli, Efficient generation of n-photon binomial states and their use in quantum gates in cavity qed, Physics Letters A 374, 2235 (2010)

2010
[53]

S. R. Miry, M. K. Tavassoly, and R. Roknizadeh, On the generation of number states, their single- and two-mode superpositions, and two-mode binomial state in a cavity, J. Opt. Soc. Am. B31, 270 (2014)

2014
[54]

Rempe, Deterministic creation of entangled atom- light Schrödinger-cat states, Nature Photonics 13, 110 (2019)

B.Hacker, S.Welte, S.Daiss, A.Shaukat, S.Ritter, L.Li, and G. Rempe, Deterministic creation of entangled atom- light Schrödinger-cat states, Nature Photonics 13, 110 (2019)

2019
[55]

H. J. Briegel and R. Raussendorf, Persistent entangle- ment in arrays of interacting particles, Phys. Rev. Lett. 86, 910 (2001)

2001
[56]

Raussendorf, D

R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A68, 022312 (2003)

2003
[57]

W. Dür, H. Aschauer, and H.-J. Briegel, Multiparticle entanglement purification for graph states, Phys. Rev. Lett. 91, 107903 (2003)

2003
[58]

M. Hein, J. Eisert, and H. J. Briegel, Multiparty entan- glement in graph states, Phys. Rev. A69, 062311 (2004)

2004
[59]

Van den Nest, J

M. Van den Nest, J. Dehaene, and B. De Moor, Graphical description of the action of local clifford transformations on graph states, Phys. Rev. A69, 022316 (2004)

2004
[60]

Aschauer, W

H. Aschauer, W. Dür, and H.-J. Briegel, Multiparticle entanglement purification for two-colorable graph states, Phys. Rev. A71, 012319 (2005)

2005
[61]

Raussendorf and H

R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett.86, 5188 (2001)

2001
[62]

Scarani, H

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, The security of practical quantum key distribution, Rev. Mod. Phys. 81, 1301 (2009)

2009
[63]

Dieks, Overlap and distinguishability of quantum states, Physics Letters A126, 303 (1988)

D. Dieks, Overlap and distinguishability of quantum states, Physics Letters A126, 303 (1988)

1988
[64]

Peres, How to differentiate between non-orthogonal states, Physics Letters A128, 19 (1988)

A. Peres, How to differentiate between non-orthogonal states, Physics Letters A128, 19 (1988)

1988
[65]

Abruzzo, S

S. Abruzzo, S. Bratzik, N. K. Bernardes, H. Kamper- mann, P. van Loock, and D. Bruß, Quantum repeaters and quantum key distribution: Analysis of secret-key rates, Phys. Rev. A87, 052315 (2013)

2013
[66]

B. T. Kirby, S. Santra, V. S. Malinovsky, and M. Brod- sky, Entanglement swapping of two arbitrarily degraded entangled states, Phys. Rev. A94, 012336 (2016)

2016
[67]

Y. Wang, M. Um, J. Zhang, S. An, M. Lyu, J.-N. Zhang, L.-M. Duan, D. Yum, and K. Kim, Single-qubit quan- tum memory exceeding ten-minute coherence time, Na- ture Photonics 11, 646 (2017)

2017
[68]

M. A. Nielsen and I. L. Chuang, Quantum Computa- tion and Quantum Information: 10th Anniversary Edi- tion (Cambridge University Press, 2010)

2010

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [40]

W. J. Munro, A. M. Stephens, S. J. Devitt, K. A. Harri- son, and K. Nemoto, Quantum communication without the necessity of quantum memories, Nature Photonics6, 777 (2012)

2012

[2] [1]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Long- distance quantum communication with atomic ensembles and linear optics, Nature414, 413 (2001). 13

work page 2001

[3] [2]

If the outcome is not|˜0+˜0+⟩, the final atomic state will be the state in Equation B20 with Pauli-Z op- eration(s) on corresponding matter qubit(s)

If nec- essary, we can get one of the Bell states(|↑↑⟩ + |↓↓⟩)/ √ 2 by performing a Hadamard operation on one of the mat- ter qubits. If the outcome is not|˜0+˜0+⟩, the final atomic state will be the state in Equation B20 with Pauli-Z op- eration(s) on corresponding matter qubit(s). Similarly, for | ˜ϕ+⟩2, | ˜ϕ+⟩3 and | ˜ϕ+⟩4, we have 1√ 2 (|↑⟩ + |↓⟩) | ˜...

work page

[4] [3]

Muralidharan, J

S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, Ultrafast and fault-tolerant quantum com- munication across long distances, Phys. Rev. Lett.112, 250501 (2014)

work page 2014

[5] [4]

Jiang, J

L. Jiang, J. M. Taylor, and M. D. Lukin, Fast and robust approach to long-distance quantum communication with atomic ensembles, Phys. Rev. A76, 012301 (2007)

2007

[6] [5]

A. S. Cacciapuoti, M. Caleffi, F. Tafuri, F. S. Cataliotti, S. Gherardini, and G. Bianchi, Quantum internet: Net- working challenges in distributed quantum computing, IEEE Network 34, 137 (2020)

work page 2020

[7] [6]

H. J. Kimble, The quantum internet, Nature453, 1023 (2008)

2008

[8] [7]

A. K. Ekert, Quantum cryptography based on bell’s the- orem, Phys. Rev. Lett.67, 661 (1991)

1991