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On the Analysis of a Multipartite Entanglement Distribution Switch

Published: 12 June 2020 Publication History

Abstract

We study a quantum switch that distributes maximally entangled multipartite states to sets of users. The entanglement switching process requires two steps: first, each user attempts to generate bipartite entanglement between itself and the switch; and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. Further, we assume that all quantum states, if generated successfully, have perfect fidelity and that decoherence is negligible. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. Via extensive use of Lyapunov functions, we derive necessary and sufficient conditions for the stability of the system and closed-form expressions for the switch capacity and the expected number of qubits in memory.

References

[1]
C. H. Bennett and G. Brassard. 2014. Quantum Cryptography: Public Key Distribution and Coin Tossing. Theor. Comput. Sci., Vol. 560, P1 (2014), 7--11.
[2]
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, Vol. 70, 13 (1993), 1895.
[3]
C. H. Bennett, G. Brassard, and N. D. Mermin. 1992. Quantum cryptography without Bell's theorem. Physical review letters, Vol. 68, 5 (1992), 557.
[4]
U. N. Bhat. 1986. Finite capacity assembly-like queues . Queueing Systems, Vol. 1, 1 (1986), 85--101.
[5]
F. Bonomi. 1987. An approximate analysis for a class of assembly-like queues . Queueing Systems, Vol. 1, 3 (1987), 289--309.
[6]
S. Bose, V. Vedral, and P. L. Knight. 1998. Multiparticle generalization of entanglement swapping . Physical Review A, Vol. 57, 2 (1998), 822.
[7]
P. Brémaud. 1999. Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues . (1999).
[8]
H-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller. 1998. Quantum repeaters: the role of imperfect local operations in quantum communication . Physical Review Letters, Vol. 81, 26 (1998), 5932.
[9]
A. Broadbent, J. Fitzsimons, and E. Kashefi. 2009. Universal blind quantum computation. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science. IEEE, 517--526.
[10]
D. Bruss, A. Ekert, S. F. Huelga, J-W. Pan, and A. Zeilinger. 1997. Quantum computing with controlled-NOT and few qubits . Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 355, 1733 (1997), 2259--2266.
[11]
K. Chen and H-K. Lo. 2004. Multi-partite quantum cryptographic protocols with noisy GHZ states . arXiv preprint quant-ph/0404133 (2004).
[12]
E. De Cuypere and D. Fiems. 2011. Performance evaluation of a kitting process. In International Conference on Analytical and Stochastic Modeling Techniques and Applications. Springer, 175--188.
[13]
A. K. Ekert. 1991. Quantum Cryptography Based on Bell's Theorem . Physical review letters, Vol. 67, 6 (1991), 661.
[14]
Z. Eldredge, M. Foss-Feig, J. A. Gross, S. L. Rolston, and A. V. Gorshkov. 2018. Optimal and secure measurement protocols for quantum sensor networks. Physical Review A, Vol. 97, 4 (2018), 042337.
[15]
M. Epping, H. Kampermann, D. Bruß, et almbox. 2017. Multi-partite entanglement can speed up quantum key distribution in networks . New Journal of Physics, Vol. 19, 9 (2017), 093012.
[16]
F. Ewert and P. van Loock. 2014. 3/4-Efficient Bell Measurement with Passive Linear Optics and Unentangled Ancillae . Physical review letters (2014).
[17]
G. Fayolle, V. A. Malyshev, and R. Iasnogorodski. 1999. Random Walks in the Quarter-Plane. Vol. 40. Springer.
[18]
G. Fayolle, V. A. Malyshev, and M. V. Menshikov. 1995. Topics in the Constructive Theory of Countable Markov Chains. Cambridge University Press.
[19]
F. G. Foster. 1953. On the Stochastic Matrices Associated with Certain Queuing Processes . The Annals of Mathematical Statistics, Vol. 24, 3 (1953), 355--360.
[20]
F. Grasselli, H. Kampermann, and D. Bruß. 2018. Finite-key effects in multipartite quantum key distribution protocols . New Journal of Physics, Vol. 20, 11 (2018), 113014.
[21]
D. M. Greenberger, M. A. Horne, and A. Zeilinger. 1989. Going beyond Bell's theorem . In Bell's theorem, quantum theory and conceptions of the universe. Springer, 69--72.
[22]
W. P. Grice. 2011. Arbitrarily Complete Bell-State Measurement Using Only Linear Optical Elements . Physical Review A (2011).
[23]
S. Guha, H. Krovi, C. A. Fuchs, Z. Dutton, J. A. Slater, C. Simon, and W. Tittel. 2015. Rate-loss analysis of an efficient quantum repeater architecture. Physical Review A, Vol. 92, 2 (2015), 022357.
[24]
J-C. Hao, C-F. Li, and G-C. Guo. 2001. Controlled dense coding using the Greenberger-Horne-Zeilinger state . Physical Review A, Vol. 63, 5 (2001), 054301.
[25]
J. M. Harrison. 1973. Assembly-like queues . Journal of Applied Probability, Vol. 10, 2 (1973), 354--367.
[26]
F. Helmer and F. Marquardt. 2009. Measurement-based synthesis of multiqubit entangled states in superconducting cavity QED . Physical Review A, Vol. 79, 5 (2009), 052328.
[27]
M. Hillery, V. Buvz ek, and A. Berthiaume. 1999. Quantum secret sharing . Physical Review A, Vol. 59, 3 (1999), 1829.
[28]
W. J. Hopp and J. T. Simon. 1989. Bounds and heuristics for assembly-like queues . Queueing systems, Vol. 4, 2 (1989), 137--155.
[29]
L. Jiang, J. M. Taylor, A. S. Sørensen, and M. D. Lukin. 2007. Distributed quantum computation based on small quantum registers. Physical Review A, Vol. 76, 6 (2007), 062323.
[30]
P. Komar, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin. 2014. A quantum network of clocks. Nature Physics, Vol. 10, 8 (2014), 582--587.
[31]
S. C. Kompalli and R. R. Mazumdar. 2009. On a Generalized Foster-Lyapunov Type Criterion for the Stability of Multidimensional Markov chains with Applications to the Slotted-Aloha Protocol with Finite Number of Queues . arXiv preprint arXiv:0906.0958 (2009).
[32]
E. H. Lipper and B. Sengupta. 1986. Assembly-like queues with finite capacity: bounds, asymptotics and approximations . Queueing Systems, Vol. 1, 1 (1986), 67--83.
[33]
P. Marks. 2007. Quantum Cryptography to Protect Swiss Election . NewScientist (15 October 2007) (2007).
[34]
S. Muralidharan, L. Li, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang. 2016. Optimal architectures for long distance quantum communication. Scientific reports, Vol. 6 (2016), 20463.
[35]
M. Pant, H. Krovi, D. Englund, and S. Guha. 2017. Rate-distance tradeoff and resource costs for all-optical quantum repeaters. Physical Review A, Vol. 95, 1 (2017), 012304.
[36]
S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi. 2017. Fundamental limits of repeaterless quantum communications. Nature communications, Vol. 8, 1 (2017), 1--15.
[37]
S. Ramachandran and D. Delen. 2005. Performance analysis of a kitting process in stochastic assembly systems . Computers & Operations Research, Vol. 32, 3 (2005), 449--463.
[38]
Z. Rosberg. 1980. A positive recurrence criterion associated with multidimensional queueing processes . Journal of Applied Probability, Vol. 17, 3 (1980), 790--801.
[39]
S. M. Ruiz. 1996. An algebraic identity leading to Wilson's theorem . The Mathematical Gazette, Vol. 80, 489 (1996), 579--582.
[40]
M. Schaffry, E. M. Gauger, J. J. L. Morton, J. Fitzsimons, S. C. Benjamin, and B. W. Lovett. 2010. Quantum metrology with molecular ensembles . Physical Review A, Vol. 82, 4 (2010), 042114.
[41]
L. I. Sennott. 1985. Tests for the nonergodicity of multidimensional Markov chains . Operations research, Vol. 33, 1 (1985), 161--167.
[42]
P. Som, W. E. Wilhelm, and R. L. Disney. 1994. Kitting process in a stochastic assembly system . Queueing Systems, Vol. 17, 3--4 (1994), 471--490.
[43]
W. Szpankowski. 1988. Stability conditions for multidimensional queueing systems with computer applications . Operations Research, Vol. 36, 6 (1988), 944--957.
[44]
M. Takeoka, S. Guha, and M. M. Wilde. 2014. Fundamental rate-loss tradeoff for optical quantum key distribution. Nature communications, Vol. 5, 1 (2014), 1--7.
[45]
W. Tittel, H. Zbinden, and N. Gisin. 2001. Experimental demonstration of quantum secret sharing . Physical Review A, Vol. 63, 4 (2001), 042301.
[46]
R. L. Tweedie. 1983. The existence of moments for stationary Markov chains . Journal of Applied Probability, Vol. 20, 1 (1983), 191--196.
[47]
R. Van Meter. 2014. Quantum Networking. John Wiley & Sons.
[48]
G. Vardoyan, S. Guha, P. Nain, and D. Towsley. 2019 a. On the Capacity Region of Bipartite and Tripartite Entanglement Switching . arXiv preprint arXiv:1901.06786 (2019).
[49]
G. Vardoyan, S. Guha, P. Nain, and D. Towsley. 2019 b. On the Stochastic Analysis of a Quantum Entanglement Switch .arxiv: 1903.04420 [quant-ph]
[50]
W. K. Wootters and W. H. Zurek. 1982. A single quantum cannot be cloned . Nature, Vol. 299, 5886 (1982), 802--803.
[51]
L. Xiao, Gui L. Long, F-G. Deng, and J-W. Pan. 2004. Efficient multiparty quantum-secret-sharing schemes . Physical Review A, Vol. 69, 5 (2004), 052307.
[52]
M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert. 1993. “Event-ready-detectors”Bell experiment via entanglement swapping . Physical Review Letters, Vol. 71 (1993), 4287--4290.
[53]
M. Zukowski, A. Zeilinger, and H. Weinfurter. 1995. Entangling Photons Radiated by Independent Pulsed Sources . Annals of the New York academy of Sciences, Vol. 755, 1 (1995), 91--102.

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cover image Proceedings of the ACM on Measurement and Analysis of Computing Systems
Proceedings of the ACM on Measurement and Analysis of Computing Systems  Volume 4, Issue 2
SIGMETRICS
June 2020
623 pages
EISSN:2476-1249
DOI:10.1145/3405833
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 12 June 2020
Online AM: 07 May 2020
Published in POMACS Volume 4, Issue 2

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Author Tags

  1. entanglement distribution
  2. markov chain
  3. quantum switch

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  • National Science Foundation

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  • (2024)Analytical Performance Estimations for Quantum Repeater Network Scenarios2024 IEEE International Conference on Quantum Computing and Engineering (QCE)10.1109/QCE60285.2024.00226(1960-1966)Online publication date: 15-Sep-2024
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