[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
Springer Nature Link
Log in

Power, Puzzles and Properties of Entanglement

  • Conference paper
  • First Online:
Machines, Computations, and Universality (MCU 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2055))

Included in the following conference series:

Abstract

Quantum entanglement is behind various puzzling/mysterious or paradoxical phenomena of quantum mechanics in general and of quantum information processing and communication (QIPC) in particular. Or, using less strong terms, quantum entanglement leads to highly nonintuitive or even counterintuitive effects. Some of them have been known for long time. New are being discovered almost daily. At the same time quantum entanglement is considered to be a very powerful resource for QIPC and, together with quantum superposition, quantum parallelism and quantum measurement, to be the main resource of the (provable) exponentially larger power of QIPC with respect to the classical information processing and communication.

It is increasingly realized that quantum entanglement is at the heart of quantum physics and as such it may be of very broad importance for modern science and future technologies. It has also been to a large extent quantum entanglement that has led in quantum mechanics to asking fundamentally new questions and has brought a chance to see in a more profound way various features of the quantum world (and this way it can contribute to a new understanding of the foundations of quantum mechanics). There is therefore a large need to understand, analyze and utilize this resource.

The aim of the paper is, on one side, to illustrate and analyze various puzzling phenomena that are due to the quantum entanglement and related nonlocality of quantum mechanics, as well as computational and, especially, communicational power of quantum entanglement. On the other side, the aim of the paper is to discuss main basic concepts, methods and results of the already very rich body of knowledge obtained recently at the attempts to understand, qualitatively and quantitatively, entanglement, laws and limitations of its distribution as well as its properties, structures and potentials for applications.

In order to demonstrate special power of quantum entanglement two puzzles “with science fiction overtones” are dealt with first. They look like exhibiting a telepathy.

Most of the paper has been written during the first author stay with the ERATO project. Support of the grants GAČR 201/01/0413, CEZ:J07/98:143300001 is also to be acknowledged.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 35.99
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 44.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. L. Accardi and M. Ohya. Teleportation of general quantum systems. Technical report, quant-ph/9912087, 1999.

    Google Scholar 

  2. S. Albeverio and S.-M. Fei. Teleportation of general finite dimensional quantum systems. Technical report, quant-ph/0012035, 2000.

    Google Scholar 

  3. J. S. Bell On the Einstein-Podolsky-Rosen paradox. Physics 1, pages 195–200, 1964. Reprinted in Quantum Theory and Measurement, (eds): J. A. Wheeler and W. H. Zurek, 403-408.

    Google Scholar 

  4. C. H. Bennett, D. DiVincenzo, J. Smolin, B. Terhal, and W. Wooters. Remote state preparation. Technical report, quant-ph/0006044, 2000.

    Google Scholar 

  5. C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal. Exact and asymptotic measures of multipartite pure state entanglement. Technical report, quant-ph/9908073, 1999.

    Google Scholar 

  6. C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal. Entanglementassisted classical capacity of noisy quantum channels. Technical report, quant ph/9904023, 1999a.

    Google Scholar 

  7. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 70:1895–1899, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. H. Bennett, G. Brassard, S. Popescu, B. W. Schumacher, J. A. Smolin, and W. K. Wootters Purification of noisy entanglement and faithful teleportation via noisy channels. Physical Review Letters, 76(5):722–725, 1996.

    Article  Google Scholar 

  9. C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Moric, E. M. Rains, P. W. Shor, and J. A. Smolin Quantifying non-locality without entanglement. Technical report, quant-ph/9804053, 1998.

    Google Scholar 

  10. C. H. Bennett, D. P. DiVincenzo, and J. A. Smolin Capacities of quantum erasure channels. Technical report, quant-ph/9701015, 1997a.

    Google Scholar 

  11. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters Mixed state entanglement and quantum error correction. Physical Review A, 54:3824–3851, 1996a. quant-ph/9604024.

    Article  MathSciNet  Google Scholar 

  12. D. Bohm. A suggested interpretation of the quantum theory in terms of “hidden” variables I and II. Physics Review, 85:166–193, 1952. also in “Quantum theory and measurements” (ed. J. A. Wheeler and W. H. Zurek), Princeton University Press, 1983.

    Google Scholar 

  13. S. Bose and D. Home. A generic source of entanglement showing complementarity between entanglemen and particle distinguishibility. Technical report, quant ph/0101093, 2000.

    Google Scholar 

  14. S. Bose and V. Vedral. Mixedeness and teleporattion. Technical report, quant ph/9912033, 1999.

    Google Scholar 

  15. S. Bose, V. Vedral, and P. L. Knight. A multiparticle generalization of entanglement swapping. Technical report, quant-ph/9708004, 1997.

    Google Scholar 

  16. J. Bouda and V. B. zek. Entanglement swapping between multi-qudit systems. Technical report, Tech. Report, Faculty of Informatics, Masaryk University, 2000.

    Google Scholar 

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

    Article  Google Scholar 

  18. G. Bowen. Classical information capacity of superdense coding. Technical report, quant-ph/0101117, 2001.

    Google Scholar 

  19. G. Brassard. Quantuqm communication complexity. Technical report, quant ph/ 0101005, 2001.

    Google Scholar 

  20. D. Bruß and A. Peres. Construction of quantum states with bound entanglement. Technical report, quant-ph/9911056, 1999.

    Google Scholar 

  21. H. Buhrman, R. Cleve, and A. Wigderson. Quantum vs. classical communication and computation. In Proceedings of 30th ACM STOC, pages 63–68, 1998. quant ph/9802040.

    Google Scholar 

  22. R. Cleve, D. Gottesman, and H.-K. Lo. How to share a quantum secret. Technical report, quant-ph/9901025, 1999.

    Google Scholar 

  23. V. Coffman, J. Kundu, and W. K. Wootters. Distributed entanglement. Technical report, quant-ph/9907047, 1999.

    Google Scholar 

  24. D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal. Unextendible product bases, uncompletable product bases, and bound entanglement. Technical report, quant-ph/9908070, 1999.

    Google Scholar 

  25. D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal. Evidence for bound entangled states with negative partial transpose. Technical report, quant-ph/9910026, 1999.

    Google Scholar 

  26. D. P. DiVincenzo, C. A. Fuchs, H. Mabuchi, J. A. Smolin, A. Thapliyal, and A. Uhlmann. Entanglement of assistance. Technical report, quant-ph/9803033, 1998.

    Google Scholar 

  27. W. Dürr. Entanglement molecules. Technical report, quant-ph/0006105, 2000.

    Google Scholar 

  28. W. Dürr and J. Cirac. Multipartite entanglement and its experimental detection. Technical report, quant-ph/0011025, 2000.

    Google Scholar 

  29. A. Einstein, B. Podolsky, and N. Rosen. Can quantum mechanical description of physics reality be considered complete? Physical Review, 47:777–780, 1935.

    Article  MATH  Google Scholar 

  30. A. K. Ekert Quantum cryptography based on Bell’s theorem. Physical Review Letters, 67(6):661–663, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  31. B. Enquist and W. Schmid, editors. Mathematics unlimited, 2001 and beyond, chapter Quantum computing challenges, pages 529–564. Springer, 2000.

    Google Scholar 

  32. V. N. Gorbachev and A. I. Trubilko. Quantum teleportation of EPR pair by three-particle entanglement. Technical report, quant-ph/9906110, 1999.

    Google Scholar 

  33. V. N. Gorbachev, A. I. Zhiliba, A. I. Trubilko, and E. S. Yakovleva. Teleportation of entangled states and dense coding using a multiparticle channel. Technical report, quant-ph/0011124, 2000.

    Google Scholar 

  34. D. Gottesman. Theory of quantum secret sharing. Technical report, quantph/9910067, 1999.

    Google Scholar 

  35. D. Gottesman and I. L. Chuang. Quantum teleportation is a universal computational primitive. Technical report, quant-ph/9908010, 1999.

    Google Scholar 

  36. D. M. Greenberger, M. A. Horne, and A. Zeilinger. Bell’s theorem and the conception of the universe, chapter Going beyond Bell’s theorem, pages 69-. Kluwer Academic, Dordrecht, 1989.

    Google Scholar 

  37. J. Gruska. Quantum computing. McGraw-Hill, 1999. See also additions and updatings of the book on http://www.mcgraw-hill.co.uk/gruska.

  38. L. Hardy. Spooky action at a distance in quantum mechanics. Contemporary physics, 6(6):419–429, 1998.

    Article  MathSciNet  Google Scholar 

  39. L. Hardy. Disentangling non-locality and teleportation. Technical report, quantph/9906123, 1999.

    Google Scholar 

  40. M. Hillery, V. Bu.zek, and A. Berthiaume. Quantum secret sharing. Technical report, quant-ph/9806063, 1998.

    Google Scholar 

  41. S. Hill and W. K. Wootters Entanglement of a pair of quantum bits. Technical report, quant-ph/9703041, 1997.

    Google Scholar 

  42. T. Hiroshima. Optimal dense coding with mixed state entanglement. Technical report, quant-ph/0009048, 2000.

    Google Scholar 

  43. M. Horodecki, P. Horodecki, and R. Horodecki. Inseperable two spin 1/2 density matrices can be distilled to a singlet form. Physics Review Letters, 78:547–577, 1997.

    Article  Google Scholar 

  44. M. Horodecki, P. Horodecki, and R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Physics Letters A, 223:1–8, 1998. quantph/9605038.

    Article  MathSciNet  Google Scholar 

  45. M. Horodecki, P. Horodecki, and R. Horodecki. Limits for entanglement measures. Technical report, quant-ph/9908065, 1999.

    Google Scholar 

  46. M. Horodecki, P. Horordecki, and R. Horodecki. Quantum information-an introduction to basic theoretical concepts and experiments, chapter Mixed-state entanglement and quantum communication. Springer, 2001.

    Google Scholar 

  47. R. Horodecki, M. Horodecki, and P. Horodecki. Reversibility of local transformations of multipartite entanglement. Technical report, quant-ph/9912039, 1999.

    Google Scholar 

  48. R. Horodecki, M. Horodecki, and P. Horodecki. On balance of information in bipartite quantum information systems: entanglement-energy analogy. Technical report, quant-ph/0002021, 2000.

    Google Scholar 

  49. M. Horodecki, P. Horodecki, and R. Horodecki. Mixed-state entanglement and distillation: is there a “bound” entanglement in nature? Technical report, quantph/9801069, 1998a.

    Google Scholar 

  50. M. Horodecki, P. Horodecki, and R. Horodecki. Bound entanglement can be activated. Technical report, quant-ph/9806058, 1998b.

    Google Scholar 

  51. M. Horodecki and R. Horodecki. Are there basic laws of quantum information processing? Technical report, quant-ph/9705003, 1997.

    Google Scholar 

  52. J. G. Jensen and R. Schack. Quantum authentication and key distribution using catalysis. Technical report, quant-ph/00031104, 2000.

    Google Scholar 

  53. I. D. Jonathan and M. B. Plenio. Entanglement-assisted local manipulation of pure quantum states. Technical report, quant-ph/9905071, 1999. See also Phys. Rev. Lett., 83, 3566–3569, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  54. R. Jozsa, D. S. A. J. P. Dowling, and C. P. Williams. Quantum clock synchronization based on shared prior entanglement. Technical report, quant-ph/0004105, 2000.

    Google Scholar 

  55. P. Kaye and M. Mosca. Quantum networks for concentrating entanglement. Technical report, quant-ph/0101009, 2001.

    Google Scholar 

  56. A. Kent. Entangled mixed states and local purification. Technical report, quantph/9805088, 1998.

    Google Scholar 

  57. A. Kent, N. Linden, and S. Massar. Optimal entanglement enhancement for mixed states. Technical report, quant-ph/9902022, 1999.

    Google Scholar 

  58. Y.-H. Kim, S. P. Kulik, and Y. Shih. Quantum teleportation with a complete Bell state measurement. Technical report, quant-ph/0010046, 2000.

    Google Scholar 

  59. M. Koashi, V. B. zek, and N. Imoto. Tight bounds for symmetric sharing of entanglement among qubits. Technical report, quant-ph/0007086, 2000.

    Google Scholar 

  60. B. Kraus and J. I. Cirac. Optimal creation of entanglement using a two-qubit gate. Technical report, quant-ph/0011050, 2000.

    Google Scholar 

  61. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki. Optimization of entanglement witnesses. Technical report, quant-ph/0005014, 2000.

    Google Scholar 

  62. N. Linden and S. Popescu. Bound entanglement and teleportation. Technical report, quant-ph/9807069, 1998.

    Google Scholar 

  63. N. Linden, S. Popescu, B. Schumacher, and M. Westmoreland. Reversibility of local transformations of multiparticle entanglement. Technical report, quantph/9912039, 1999.

    Google Scholar 

  64. L. Marinatto and T. Weber. Which kind of two-particles states can be teleported through a three-particle quantum channel? Technical report, quant-ph/0004054, 2000.

    Google Scholar 

  65. M. Murao and V. Vedral. Remote information concentration using a bound entangled state. Technical report, quant-ph/0008078, 2000.

    Google Scholar 

  66. M. A. Nielsen. On the units of bipartite entanglement: is sixten ounces of entanglement always equal to one pound? Technical report, quant-ph/0011063, 2000.

    Google Scholar 

  67. M. A. Nielsen and J. Kempe. Separable states are more disordered globally than locally. Technical report, quant-ph/0011117, 2000.

    Google Scholar 

  68. M. Nielsen A partial order on the entangled states. Technical report, quantph/9811053, 1998.

    Google Scholar 

  69. K. M. O. Connors and W. K. Wooters. Entangled rings. Technical report, quantph/0009041, 2000.

    Google Scholar 

  70. A.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger. Experimental test of quantum non-loclaity in three photon Greenberg-Horne-Zeilinger entanglement. Nature, 403:515–519, 2000.

    Article  Google Scholar 

  71. J. W. Pan, D. Bouwemester, H. Weinfurter, and A. Zeilinger. Experimental entanglement swapping: entangled photons that never interacted. Physical Review Letters, 80:3891–3894, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  72. J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger. Feasible entanglement purification for quantum communication. Technical report, Institut für Experimentalphysik, universityät Wien, 2000.

    Google Scholar 

  73. A. K. Pati. Quantum cobweb: remote shared-entangling of an unknown quantum state. Technical report, quant-ph/0101049, 2001.

    Google Scholar 

  74. I. C. Percival. Why Bell experiments. Technical report, quant-ph/0008097, 2000.

    Google Scholar 

  75. A. Peres. Separability criterion for density matrices. Physical Review Letters, 77:1413–1415, 1996a.

    Article  MATH  MathSciNet  Google Scholar 

  76. A. Peres. Delayed choice for entanglement swapping. Journal of Modern Optics, 47:139–143, 2000.

    MathSciNet  Google Scholar 

  77. M. Plenio and V. Vedral. Bounds on relative entropy of entanglement for multiparty systems. Technical report, quant-ph/0010080, 2000.

    Google Scholar 

  78. M. B. Plenio and V. Vedral. Teleporatation, entanglement and thermodynamics in the quantum world. Technical report, quant-ph/9804075, 1998.

    Google Scholar 

  79. R. Rausschendorf and H. Briegel. Quantum computing via measurements only. Technical report, quant-ph/0010033, 2000.

    Google Scholar 

  80. R. Raz. Exponential separation of quantum and classical communication complexity. In Proceedings of 31st ACM STOC, pages 358–367, 1999.

    Google Scholar 

  81. O. Rudolp. A new class of entanglement measures. Technical report, quantph/0005011, 2000.

    Google Scholar 

  82. E. Schrödinger. Die gegenwartige situation in der quanenmechanik. Natürwissenschaften, 23:807–812, 823-828, 844-849, 1935.

    Article  Google Scholar 

  83. P. Shor and J. S. an A. Thapliyal. Superactivation of bound entanglement. Technical report, quant-ph/0005117, 2000.

    Google Scholar 

  84. J. A. Smolin. A four-party unlockable bound-entangled state. Technical report, quant-ph/0001001, 2000.

    Google Scholar 

  85. H. P. Stapp. From quantum non-locality to mind-brain interactions. Technical report, quant-ph/0010029, 2000.

    Google Scholar 

  86. A. M. Steane and W. van Dam. Guess my number. Physics Today, 53(2):35–39, 2000.

    Article  Google Scholar 

  87. B. M. Terhal. Detecting quantum entanglement. Technical report, quantph/ 0101032, 2001.

    Google Scholar 

  88. B. M. Terhal, D. P. DiVincenzo, and D. W. Leung. Hidding bits in Bell states. Technical report, quant-ph/0011042, 2000.

    Google Scholar 

  89. W. Tittel, T. Brendel, H. Zbinden, and N. Gisin. Quantum cryptography using entangled photons in energy-time Bell states. Physics Review Letters, 84:4737–4740, 2000.

    Article  Google Scholar 

  90. W. Tittel, H. Zbinden, and N. Gisin. Quantum secret sharing using pseudo-GHZ states. Technical report, quant-ph/9912035, 1999.

    Google Scholar 

  91. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin. Experimental demonstration of quantum correlation over more than 10km. Physical Review A, 57(5):3229–3232, 1998. Preprint quant-ph/9806043.

    Article  Google Scholar 

  92. A. Uhlmann. Entropy and optimal decomposition of states relative to a maximal commutative algebra. Technical report, quant-ph/9704017, 1997.

    Google Scholar 

  93. L. Vaidman. Teleportation: dream or reality? Technical report, quantph/9810089, 1998.

    Google Scholar 

  94. W. van Dam, P. Høyer, and A. Tapp. Multiparty quantum communication complexity. Technical report, quant-ph/9710054, 1997.

    Google Scholar 

  95. V. Vedral and M. B. Plenio Entanglement measures and purification procedures. Technical report, quant-ph/9707035, 1997.

    Google Scholar 

  96. J. Walgate, A. J. Short, L. Hardy, and V. Vedral. Local distinguishability of multipartite orthogonal quantum states. Technical report, quant-ph/0007098, 2000.

    Google Scholar 

  97. A. M. Wang. Bounds on the generalized entanglement of formation for multiparity systems. Technical report, quant-ph/0011091, 2000.

    Google Scholar 

  98. A. M. Wang. Improved relative entropy of entanglement for multi-party systems. Technical report, quant-ph/0012029, 2000a.

    Google Scholar 

  99. R. F. Werner. All teleportation and dense coding schemes. Technical report, quant-ph/0003070, 2000.

    Google Scholar 

  100. W. K. Wootters. Entangled chains. Technical report, quant-ph/0001114, 2000.

    Google Scholar 

  101. M. Žukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert. “Event-ready-detectors”; Bell experiments via entanglement swapping. Physical Review Letters, 71:4287–4290, 1993.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ERATO project, University of Tokyo, Hongon 5-28-3, Bunkyo-ku, Tokyo, 113-0033, Japan

    Jozef Gruska & Hiroshi Imai

  2. Faculty of Informatics, Masaryk University, Botanická 68a, 602 00, Brno, Czech Republic

    Jozef Gruska

Authors
  1. Jozef Gruska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroshi Imai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LITA, UFR MIM, Université de Metz, Ile du Saulcy, 57045, Metz, Cedex, France

    Maurice Margenstern

  2. Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, 5 Academiei str, 2028, Chiŗinău, Moldova

    Yurii Rogozhin

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gruska, J., Imai, H. (2001). Power, Puzzles and Properties of Entanglement. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_3

Download citation

  • DOI: https://doi.org/10.1007/3-540-45132-3_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42121-4

  • Online ISBN: 978-3-540-45132-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation