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arxiv: 2405.18066 · v1 · submitted 2024-05-28 · 🪐 quant-ph · cs.NI· cs.PF

An on-demand resource allocation algorithm for a quantum network hub and its performance analysis

Scarlett Gauthier , Thirupathaiah Vasantam , Gayane Vardoyan This is my paper

Pith reviewed 2026-05-24 01:25 UTC · model grok-4.3

classification 🪐 quant-ph cs.NIcs.PF
keywords quantum networksentanglement generation switchresource allocationErlang loss systemblocking probabilityinsensitivity theoremqueueing theoryPoisson arrivals
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The pith

The demand blocking probability at a quantum entanglement generation switch depends only on the mean durations of attempts and calibrations.

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

The paper models an Entanglement Generation Switch as an Erlang loss system in which user demands for entanglement arrive according to a Poisson process. It derives explicit formulas for the blocking probability under three traffic scenarios and proves an insensitivity theorem showing that the probability depends solely on the average lengths of entanglement generation attempts and calibration periods. A sympathetic reader would care because the result supplies a simple analytic tool for predicting and tuning performance of shared quantum network resources without requiring the full timing distributions.

Core claim

The paper establishes that an on-demand resource allocation algorithm at an EGS, represented as an Erlang loss system with batch entanglement attempts interleaved by calibration periods, yields a demand blocking probability that is insensitive to the underlying distributions of attempt and calibration durations and depends only on their means, as derived from applied probability and queueing theory for three traffic scenarios.

What carries the argument

The mapping of the EGS to an Erlang loss system, which permits direct application of standard blocking formulas and the insensitivity property of loss systems.

Load-bearing premise

The model assumes demands arrive according to a Poisson process and that the EGS behaves exactly as an Erlang loss system with immediate allocation or blocking.

What would settle it

Collect empirical blocking rates from a physical EGS while varying the variance of attempt or calibration durations around fixed means and check whether the rates remain unchanged and match the mean-only formulas.

Figures

Figures reproduced from arXiv: 2405.18066 by Gayane Vardoyan, Scarlett Gauthier, Thirupathaiah Vasantam.

Figure 1
Figure 1. Figure 1: A simple quantum network with end nodes 𝐴 and 𝐶 wishing to share entanglement, and an intermediate node 𝐵 assisting them with the task. Initially, two entangled links – |Ψ + ⟩𝐴𝐵 between 𝐴 and 𝐵 and |Ψ + ⟩𝐵𝐶 between 𝐵 and 𝐶 – are established. 𝐵 then performs a swapping operation to directly entangle 𝐴 and 𝐶’s qubits. Depending on the distance between𝐴 and𝐶, direct generation of entanglement (without an inte… view at source ↗
Figure 2
Figure 2. Figure 2: Entanglement generation with a Bell state analyzer. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Intermediate quantum network nodes leverag [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Strict resource reservation service model. A session consists of multiple EPR pair generation attempts, [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A session from the single EPR pair generation strict resource reservation ser￾vice model, shown at the level of periods in [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A session from the multiple EPR pair generation strict resource reserva￾tion service model, shown at the level of periods in [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Service model with resource relinquishment and jump-over blocking. A session consists of multiple [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the aver￾age blocking probability per flow according to (22) with simulations for an EGS with one resource, con￾nected to eight nodes, and serving [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Average blocking probability for the first call [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of the strict and jump-over service models, for an EGS with one resource, serving [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of the request blocking probabilities of the strict sin￾gle and strict multiple service modes when there is a high probability (𝑝gen = 0.001) that an attempt to generate entanglement succeeds. Data is obtained from discrete simulations of an EGS with one resource, serving eight nodes with 8 2  = 28 flows. Ev￾ery node is restricted to a single com￾munication qubit. Session traffic is ho￾mogeneo… view at source ↗
Figure 14
Figure 14. Figure 14: Heatmaps of the average blocking proba￾bility per flow when the number of communica￾tion qubits per node and the request arrival rates are varied. Data results from numeric evaluation of (22) for an EGS with eight nodes and serving [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Non-homogeneous traffic, strict single service model: An EGS with one resource is connected to [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Communication sequence for the CI generation protocol. The field [PITH_FULL_IMAGE:figures/full_fig_p032_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Communication sequence for HE protocol. The field [PITH_FULL_IMAGE:figures/full_fig_p033_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Heatmaps of the average blocking probability per flow when the number of communication qubits [PITH_FULL_IMAGE:figures/full_fig_p035_18.png] view at source ↗
read the original abstract

To effectively support the execution of quantum network applications for multiple sets of user-controlled quantum nodes, a quantum network must efficiently allocate shared resources. We study traffic models for a type of quantum network hub called an Entanglement Generation Switch (EGS), a device that allocates resources to enable entanglement generation between nodes in response to user-generated demand. We propose an on-demand resource allocation algorithm, where a demand is either blocked if no resources are available or else results in immediate resource allocation. We model the EGS as an Erlang loss system, with demands corresponding to sessions whose arrival is modelled as a Poisson process. To reflect the operation of a practical quantum switch, our model captures scenarios where a resource is allocated for batches of entanglement generation attempts, possibly interleaved with calibration periods for the quantum network nodes. Calibration periods are necessary to correct against drifts or jumps in the physical parameters of a quantum node that occur on a timescale that is long compared to the duration of an attempt. We then derive a formula for the demand blocking probability under three different traffic scenarios using analytical methods from applied probability and queueing theory. We prove an insensitivity theorem which guarantees that the probability a demand is blocked only depends upon the mean duration of each entanglement generation attempt and calibration period, and is not sensitive to the underlying distributions of attempt and calibration period duration. We provide numerical results to support our analysis. Our work is the first analysis of traffic characteristics at an EGS system and provides a valuable analytic tool for devising performance driven resource allocation algorithms.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 2 minor

Summary. The manuscript models an Entanglement Generation Switch (EGS) as an Erlang loss system under Poisson demand arrivals and proposes an on-demand resource allocation algorithm that either blocks or immediately allocates resources. It derives closed-form expressions for demand blocking probability in three traffic scenarios, proves an insensitivity theorem establishing that blocking depends only on the means of attempt and calibration durations (not their full distributions), and supplies numerical results validating the analysis.

Significance. If the results hold, the work supplies the first analytic treatment of traffic at an EGS and a practical tool for performance-driven resource allocation in quantum networks. Credit is due for grounding the model in standard M/G/c/c loss-system theory and for explicitly invoking the insensitivity property rather than relying on simulation alone.

minor comments (2)
  1. [Abstract] Abstract: the three traffic scenarios are referenced but not named or briefly characterized, which would improve immediate readability for readers outside queueing theory.
  2. [Model description] The mapping of batch attempts plus interleaved calibrations onto a single effective holding time whose mean is used in the Erlang-B formula should be stated with an explicit equation reference in the model section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of our contributions, and recommendation to accept. We are pleased that the work is recognized as providing the first analytic treatment of traffic at an EGS using standard loss-system theory.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper maps the EGS to a standard Erlang loss system (M/G/c/c) with Poisson arrivals and derives blocking probabilities plus an insensitivity result via established queueing theory. The insensitivity theorem invoked is the classical result that stationary distribution in loss systems depends only on mean holding time, which is an external, independently verified fact from applied probability (not derived or fitted within the paper). No self-citations are load-bearing, no parameters are fitted then renamed as predictions, and no ansatz or uniqueness claim reduces to the paper's own inputs. The derivation chain is an application of known theorems to the quantum-network setting and remains self-contained.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The analysis rests on standard queueing-theory assumptions applied to the quantum hub context; no new physical entities are postulated and no parameters are fitted to data within the paper itself.

free parameters (3)
  • demand arrival rate
    Input parameter for the Poisson process; treated as given rather than fitted.
  • mean attempt duration
    Model input whose mean enters the blocking formula; not derived or fitted inside the paper.
  • mean calibration duration
    Model input whose mean enters the blocking formula; not derived or fitted inside the paper.
axioms (3)
  • domain assumption Demands arrive according to a Poisson process
    Invoked when mapping user requests to the Erlang loss model.
  • domain assumption System is an Erlang loss system (blocked calls cleared, no queue)
    Core modeling choice stated when describing on-demand allocation.
  • domain assumption Resources allocated in batches of attempts separated by calibration periods
    Reflects practical quantum switch operation as described in the model section.

pith-pipeline@v0.9.0 · 5815 in / 1627 out tokens · 45461 ms · 2026-05-24T01:25:31.730646+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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Works this paper leans on

48 extracted references · 48 canonical work pages · cited by 1 Pith paper

  1. [1]

    Arright and L

    P. Arright and L. Salvail. 2006. Blind Quantum Computation. International Journal of Quantum Information 04, 05 (2006), 883–898

    work page 2006

  2. [2]

    H Bennett, G

    C. H Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K Wootters. 1993. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical review letters 70, 13 (1993), 1895

    work page 1993

  3. [3]

    C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters. 1996. Purification of noisy entanglement and faithful teleportation via noisy channels. Physical review letters 76, 5 (1996), 722

    work page 1996

  4. [4]

    Bernien, B

    H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson. 2013. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 7447 (April 2013), 86–90

    work page 2013

  5. [5]

    R. C. Berrevoets, T. Middelburg, R. F. L. Vermeulen, L. D. Chiesa, F. Broggi, S. Piciaccia, R. Pluis, P. Umesh, J. F. Marques, W. Tittel, and J. A. Slater. 2022. Deployed measurement-device independent quantum key distribution and Bell-state measurements coexisting with standard internet data and networking equipment. Communications Physics 5, 1 (2022),

    work page 2022

  6. [6]

    https://doi.org/10.1038/s42005-022-00964-6

    work page doi:10.1038/s42005-022-00964-6

  7. [7]

    T. Bonald. 2006. Insensitive Queueing Models for Communication Networks. In Proceedings of the 1st International Conference on Performance Evaluation Methodolgies and Tools (Pisa, Italy) (valuetools ’06). Association for Computing Machinery, New York, NY, USA, 57–es. https://doi.org/10.1145/1190095.1190168

    work page doi:10.1145/1190095.1190168 2006

  8. [8]

    T. Bonald. 2006. The Erlang model with non-Poisson call arrivals. ACM SIGMETRICS Performance Evaluation Review 34, 1 (2006), 276–286

    work page 2006

  9. [9]

    Bouwmeester, J-W

    D. Bouwmeester, J-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger. 1997. Experimental quantum teleportation. Nature 390, 6660 (1997), 575–579

    work page 1997

  10. [10]

    S. L. Braunstein and A. Mann. 1995. Measurement of the Bell operator and quantum teleportation. Physical Review A 51, 3 (1995), R1727

    work page 1995

  11. [11]

    S. L. Braunstein and S. Pirandola. 2012. Side-Channel-Free Quantum Key Distribution. Phys. Rev. Lett. 108 (Mar 2012), 130502. Issue 13. https://doi.org/10.1103/PhysRevLett.108.130502

    work page doi:10.1103/physrevlett.108.130502 2012

  12. [12]

    Dynamic transitive closure via dynamic matrix inverse

    A. Broadbent, J. Fitzsimons, and E. Kashefi. 2009. Universal Blind Quantum Computation. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science . IEEE, Atlanta, Georgia, USA, 517–526. https://doi.org/10.1109/focs. 2009.36

    work page doi:10.1109/focs 2009

  13. [13]

    Cabrillo, J

    C. Cabrillo, J. I. Cirac, P. García-Fernández, and P. Zoller. 1999. Creation of entangled states of distant atoms by interference. Phys. Rev. A 59 (Feb. 1999), 1025–1033. Issue 2

    work page 1999

  14. [14]

    B. H. Charles and G. Brassard. 2014. Quantum cryptography: Public key distribution and coin tossing. Theoretical Computer Science 560 (Dec. 2014), 7–11. An on-demand resource allocation algorithm for a quantum network hub and its performance analysis

    work page 2014

  15. [15]

    C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble. 2005. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature 438, 7069 (Dec. 2005), 828–832

    work page 2005

  16. [16]

    C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble. 2007. Functional Quantum Nodes for Entanglement Distribution over Scalable Quantum Networks. Science 316, 5829 (June 2007), 1316–1320. https://doi.org/10.1126/science.1140300

    work page doi:10.1126/science.1140300 2007

  17. [17]

    W. Dai, A. Rinaldi, and D. Towsley. 2022. The Capacity Region of Entanglement Switching: Stability and Zero Latency. In 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) . IEEE, Broomfield, CO, USA, 389–399. https://doi.org/10.1109/QCE53715.2022.00060

    work page doi:10.1109/qce53715.2022.00060 2022

  18. [18]

    Deutsch, A

    D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera. 1996. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Physical review letters 77, 13 (1996), 2818

    work page 1996

  19. [19]

    L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller. 2001. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 6862 (Nov. 2001), 413–418

    work page 2001

  20. [20]

    A. K. Ekert. 1991. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67 (Aug. 1991), 661–663. Issue 6. https://doi.org/10.1103/PhysRevLett.67.661

    work page doi:10.1103/physrevlett.67.661 1991

  21. [21]

    A. K. Erlang. 1917. Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. Post Office Electrical Engineer’s Journal 10 (1917), 189–197

    work page 1917

  22. [22]

    Gauthier, G

    S. Gauthier, G. Vardoyan, and S. Wehner. 2023. An Architecture for Control of Entanglement Generation Switches in Quantum Networks. IEEE Transactions on Quantum Engineering 4 (2023), 1–17. https://doi.org/10.1109/TQE.2023. 3320047

    work page doi:10.1109/tqe.2023 2023

  23. [23]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone. 2001. Quantum-enhanced positioning and clock synchronization. Nature 412, 6845 (2001), 417–419

    work page 2001

  24. [24]

    Gottesman, T

    D. Gottesman, T. Jennewein, and S. Croke. 2012. Longer-Baseline Telescopes Using Quantum Repeaters. Phys. Rev. Lett. 109 (Aug 2012), 070503. Issue 7. https://doi.org/10.1103/PhysRevLett.109.070503

    work page doi:10.1103/physrevlett.109.070503 2012

  25. [25]

    X. Guo, C. R Breum, J. Borregaard, S. Izumi, M. V Larsen, T. Gehring, M. Christandl, J. S Neergaard-Nielsen, and U. L Andersen. 2020. Distributed quantum sensing in a continuous-variable entangled network. Nature Physics 16, 3 (2020), 281–284

    work page 2020

  26. [26]

    P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson. 2018. Deterministic delivery of remote entanglement on a quantum network. Nature 558, 7709 (June 2018), 268–273. https://doi.org/10.1038/s41586-018-0200-5

    work page doi:10.1038/s41586-018-0200-5 2018

  27. [27]

    F. Kelly. 1997. Charging and rate control for elastic traffic. European transactions on Telecommunications 8, 1 (1997), 33–37

    work page 1997

  28. [28]

    Kómár, E

    P. Kómár, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin. 2014. A quantum network of clocks. Nature Physics 10, 8 (June 2014), 582–587

    work page 2014

  29. [29]

    Krutyanskiy, M

    V. Krutyanskiy, M. Galli, V. Krcmarsky, S. Baier, D. A. Fioretto, Y. Pu, A. Mazloom, P. Sekatski, M. Canteri, M. Teller, J. Schupp, J. Bate, M. Meraner, N. Sangouard, B. P. Lanyon, and T. E. Northup. 2023. Entanglement of Trapped-Ion Qubits Separated by 230 Meters.Phys. Rev. Lett.130 (Feb. 2023), 050803. Issue 5. https://doi.org/10.1103/PhysRevLett.130.050803

    work page doi:10.1103/physrevlett.130.050803 2023

  30. [30]

    Leichtle, L

    D. Leichtle, L. Music, E. Kashefi, and H. Ollivier. 2021. Verifying BQP Computations on Noisy Devices with Minimal Overhead. PRX Quantum 2 (Oct 2021), 040302. Issue 4. https://doi.org/10.1103/PRXQuantum.2.040302

    work page doi:10.1103/prxquantum.2.040302 2021

  31. [31]

    H-K. Lo, M. Curty, and B. Qi. 2012. Measurement-Device-Independent Quantum Key Distribution. Phys. Rev. Lett. 108 (Mar 2012), 130503. Issue 13. https://doi.org/10.1103/PhysRevLett.108.130503

    work page doi:10.1103/physrevlett.108.130503 2012

  32. [32]

    H. Lu, C-H. F. Fung, and Q-Y. Cai. 2013. Two-way deterministic quantum key distribution against detector-side-channel attacks. Phys. Rev. A 88 (Oct 2013), 044302. Issue 4. https://doi.org/10.1103/PhysRevA.88.044302

    work page doi:10.1103/physreva.88.044302 2013

  33. [33]

    Makarov, A

    V. Makarov, A. Anisimov, and J. Skaar. 2006. Effects of detector efficiency mismatch on security of quantum cryptosys- tems. Phys. Rev. A 74 (Aug 2006), 022313. Issue 2. https://doi.org/10.1103/PhysRevA.74.022313

    work page doi:10.1103/physreva.74.022313 2006

  34. [34]

    Maunz, D

    P. Maunz, D. L. Moehring, S. Olmschenk, K. C. Younge, D. N. Matsukevich, and C. Monroe. 2007. Quantum interference of photon pairs from two remote trapped atomic ions. Nature Physics 3, 8 (2007), 538–541

    work page 2007

  35. [35]

    Michler, K

    M. Michler, K. Mattle, H. Weinfurter, and A. Zeilinger. 1996. Interferometric Bell-state analysis. Physical Review A 53, 3 (1996), R1209

    work page 1996

  36. [36]

    W. J. Munro, K. Azuma, K. Tamaki, and K. Nemoto. 2015. Inside quantum repeaters. IEEE Journal of Selected Topics in Quantum Electronics 21, 3 (2015), 78–90

    work page 2015

  37. [37]

    N. K. Panigrahy, T. Vasantam, D. Towsley, and L. Tassiulas. 2023. On the capacity region of a quantum switch with entanglement purification. In IEEE INFOCOM 2023-IEEE Conference on Computer Communications . IEEE, IEEE, New York, NY, USA, 1–10

    work page 2023

  38. [38]

    Pompili, S

    M. Pompili, S. L. N. Hermans, S. Baier, H. K. C. Beukers, P. C. Humphreys, R. N. Schouten, R. F. L. Vermeulen, M. J. Tiggelman, L. dos Santos Martins, B. Dirkse, S. Wehner, and R. Hanson. 2021. Realization of a multinode quantum network of remote solid-state qubits. Science 372, 6539 (April 2021), 259–264. Scarlett Gauthier, Thirupathaiah Vasantam, Gayane...

    work page 2021

  39. [39]

    Preskill

    J. Preskill. 2018. Quantum Computing in the NISQ era and beyond. Quantum 2 (Aug. 2018), 79. https://doi.org/10. 22331/q-2018-08-06-79

    work page 2018

  40. [40]

    Richard Serfozo. 1999. Introduction to Stochastic Networks . Springer, New York, NY, USA. https://doi.org/10.1007/978- 1-4612-1482-3

    work page doi:10.1007/978- 1999

  41. [41]

    B. A. Sevast’yanov. 1957. An ergodic theorem for Markov processes and its application to telephone systems with refusals. Theory of Probability & Its Applications 2, 1 (1957), 104–112

    work page 1957

  42. [42]

    van Leent, M

    T. van Leent, M. Bock, F. Fertig, R. Garthoff, S. Eppelt, Y. Zhou, P. Malik, M. Seubert, T. Bauer, W. Rosenfeld, W. Zhang, C. Becher, and H. Weinfurter. 2022. Entangling single atoms over 33 km telecom fibre. Nature 607, 7917 (July 2022), 69–73

    work page 2022

  43. [43]

    Vardoyan, S

    G. Vardoyan, S. Guha, P. Nain, and D. Towsley. 2020. On the exact analysis of an idealized quantum switch.Performance Evaluation 144 (2020), 102141

    work page 2020

  44. [44]

    Vardoyan, S

    G. Vardoyan, S. Guha, P. Nain, and D. Towsley. 2021. On the Stochastic Analysis of a Quantum Entanglement Distribution Switch. IEEE Transactions on Quantum Engineering 2 (2021), 1–16

    work page 2021

  45. [45]

    Vasantam and D

    T. Vasantam and D. Towsley. 2022. A throughput optimal scheduling policy for a quantum switch. In Quantum Computing, Communication, and Simulation II , Philip R. Hemmer and Alan L. Migdall (Eds.), Vol. 12015. International Society for Optics and Photonics, SPIE, San Francisco, CA, USA, 1201505. https://doi.org/10.1117/12.2616950

    work page doi:10.1117/12.2616950 2022

  46. [46]

    Walther and A

    P. Walther and A. Zeilinger. 2005. Experimental realization of a photonic Bell-state analyzer. Physical Review A 72, 1 (2005), 010302

    work page 2005

  47. [47]

    W. Whitt. 1980. Continuity of Generalized Semi-Markov Processes. Mathematics of Operations Research - MOR 5 (11 1980), 494–501. https://doi.org/10.1287/moor.5.4.494

    work page doi:10.1287/moor.5.4.494 1980

  48. [48]

    multiple EPR pair generation with strict resource reservation

    Y. Zhao, C-H. F. Fung, B. Qi, C. Chen, and H-K. Lo. 2008. Quantum hacking: Experimental demonstration of time- shift attack against practical quantum-key-distribution systems. Phys. Rev. A 78 (Oct 2008), 042333. Issue 4. https: //doi.org/10.1103/PhysRevA.78.042333 A PROBABILITY OF REACHING A QUEUE IN SINGLE EPR PAIR GENERATION MODE In this appendix, we de...

    work page doi:10.1103/physreva.78.042333 2008