Skip to main content

Teleportation of Quantum States

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Synonyms

Quantum teleportation; Teleportation

Years and Authors of Summarized Original Work

  • 1993; Bennett, Brassard, Crepeau, Jozsa, Peres, Wootters

Problem Definition

Suppose there are two spatially separated parties Alice and Bob and Alice wants to send a quantum state consisting of n quantum bits (qubits) ρ to Bob. Since classical communication is much more reliable, and possibly cheaper, than quantum communication, it is desirable that this task be achieved by communicating just classical bits. Such a procedure is referred to as teleportation.

Unfortunately, it is easy to argue that this is in fact not possible if arbitrary quantum states need to be communicated faithfully. However, Bennett, Brassard, Crepeau, Jozsa, Peres, and Wootters [8] presented a nice solution to it by modifying the assumptions about the resources that are available to Alice and Bob.

Key Results

Let \(\{\vert 0\rangle,\vert 1\rangle \}\)be the standard basis for the state space of one quantum bit (which is...

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover 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

Recommended Reading

  1. Anshu A, Devabathini VK, Jain R (2014) Near optimal bounds on quantum communication complexity of single-shot quantum state redistribution. http://arxiv.org/abs/1410.3031

  2. Ambainis A, Mosca M, Tapp A, de Wolf R (2000) Private quantum channels. In: Proceedings of the 41st annual IEEE symposium on foundations of computer science, Redondo Beach, pp 547–553

    Google Scholar 

  3. Boschi D, Branca S, Martini FD, Hardy L, Popescu S (1998) Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolski-Rosen channels. Phys Rev Lett 80:1121–1125

    Article  MathSciNet  MATH  Google Scholar 

  4. Berta M, Christandl M, Touchette D (2014) Smooth entropy bounds on one-shot quantum state redistribution. http://arxiv.org/abs/1409.4338

  5. Berta M (2009) Single-shot quantum state merging. Master’s thesis, ETH Zurich

    Google Scholar 

  6. Broadbent A, Fitzsimons J, Kashefi E (2009) Universal blind quantum computation. In: Proceedings of the 50th annual IEEE symposium on foundations of computer science, Atlanta

    Google Scholar 

  7. Baur M, Fedorov A, Steffen L, Filipp S, da Silva MP, Wallraff A (2012) Benchmarking a quantum teleportation protocol in superconducting circuits using tomography and an entanglement witness. Phys Rev Lett 108(4):040502

    Article  Google Scholar 

  8. Bennett C, Brassard G, Crepeau C, Jozsa R, Peres R, Wootters W (1993) Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett 70:1895–1899

    Article  MathSciNet  MATH  Google Scholar 

  9. Bennett CH, Hayden P, Leung W, Shor PW, Winter A (2005) Remote preparation of quantum states. IEEE Trans Inf Theory 51:56–74

    Article  MathSciNet  MATH  Google Scholar 

  10. Bouwmeester D, Pan JW, Mattle K, Eible M, Weinfurter H, Zeilinger A (1997) Experimental quantum teleportation. Nature 390(6660):575–579

    Article  Google Scholar 

  11. Boykin PO, Roychowdhury V (2003) Optimal encryption of quantum bits. Phys Rev A 67:042317

    Article  Google Scholar 

  12. Chaung IL, Gottesman D (1999) Quantum teleportation is a universal computational primitive. Nature 402:390–393

    Article  Google Scholar 

  13. Datta N, Hsieh M-H, Oppenheim J (2014) An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution. http://arxiv.org/abs/1409.4352

  14. Devetak I, Yard J (2008) Exact cost of redistributing multipartite quantum states. Phys Rev Lett 100:230501

    Article  Google Scholar 

  15. Fu L (2010) Electron teleportation via Majorana bound states in a mesoscopic superconductor. Phys Rev Lett 104(5):056402

    Article  Google Scholar 

  16. Herder C, http://www.scottaaronson.com/showcase2/report/charles-herder.pdf

  17. Horodecki M, Oppenheim J, Winter A (2007) Quantum state merging and negative information. Commun Math Phys 269:107–136

    Article  MathSciNet  MATH  Google Scholar 

  18. Jain R (2006) Resource requirements of private quantum channels and consequence for oblivious remote state preparation. Technical report, arXive:quant-ph/0507075

    Google Scholar 

  19. Knill E (2005) Quantum computing with realistically noisy devices. Nature 434:39–44

    Article  Google Scholar 

  20. Krauter H, Salart D, Muschik CA, Petersen JM, Shen JM, Fernholz T, Polzik ES (2013) Deterministic quantum teleportation between distant atomic objects. Nat Phys 9:400–404

    Article  Google Scholar 

  21. Lo H-K (2000) Classical communication cost in distributed quantum information processing – a generalization of quantum communication complexity. Phys Rev A 62:012313

    Article  Google Scholar 

  22. Nielsen M, Chuang I (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge/New York

    MATH  Google Scholar 

  23. Nielsen MA (2005) Cluster-state quantum computation. http://arxiv.org/abs/quant-ph/0504097

  24. Nielsen MA, Knill E, Laflamme R (1998) Complete quantum teleportation using nuclear magnetic resonance. Nature 396(6706):52–55

    Article  Google Scholar 

  25. Ursin R, Jennewein T, Aspelmeyer M, Kaltenbaek R, Lindenthal M, Zeilinger A (2004) Quantum teleportation link across the danube. Nature 430:849

    Article  Google Scholar 

  26. Yard JT, Devetak I (2009) Optimal quantum source coding with quantum side information at the encoder and decoder. IEEE Trans Inf Theory 55:5339–5351

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anurag Anshu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Anshu, A., Devabathini, V.K., Jain, R., Mukhopadhyay, P. (2016). Teleportation of Quantum States. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_421

Download citation

Publish with us

Policies and ethics