Skip to main content
SpringerLink
Log in

Broadcasting of entanglement via orthogonal and non-orthogonal state-dependent cloners

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this work, we extensively study the problem of broadcasting of entanglement as state-dependent versus state-independent cloners. We start by re-conceptualizing the idea of state-dependent quantum cloning machine (SD-QCM), and in that process, we introduce different types of SD-QCMs, namely orthogonal and non-orthogonal cloners. We derive the conditions for which the fidelity of these cloners will become independent of the input state. We note that such a construction allows us to maximize the cloning fidelity at the cost of having partial information of the input state. In the discussion on broadcasting of entanglement, we start with a general two-qubit state as our resource and later we consider a specific example of Bell diagonal state. We apply both state-dependent and state-independent cloners (orthogonal and non-orthogonal), locally and non-locally, on input resource state and obtain a range for broadcasting of entanglement in terms of the input state parameters. Our results highlight several instances where the state-dependent cloners outperform their state-independent counterparts in broadcasting entanglement. Our study provides a comparative perspective on the broadcasting of entanglement via cloning in two-qubit scenario, when we have some knowledge of the resource ensemble versus a situation when we have no such information.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)

    ADS  MATH  Google Scholar 

  2. Einstein, A.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    ADS  MATH  Google Scholar 

  3. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    ADS  MATH  Google Scholar 

  4. Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)

    ADS  Google Scholar 

  5. Bennett, C.H., Brassard, G.: Quantum cryptography. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984 (IEEE, New York, 1984) pp. 175–179

  6. Shor, P.W., Preskill, J.: Simple proof of security of the bb84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441 (2000)

    ADS  Google Scholar 

  7. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    ADS  MathSciNet  MATH  Google Scholar 

  8. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  9. Sazim, S., Chiranjeevi, V., Chakrabarty, I., Srinathan, K.: Retrieving and routing quantum information in a quantum network. Quant. Inf. Proc. 14, 4651 (2015)

    MathSciNet  MATH  Google Scholar 

  10. Adhikari, S., Chakrabarty, I., Agrawal, P.: Probabilistic secret sharing through noisy quantum channels. arXiv preprint arXiv:1012.5570 (2010)

  11. Ray, M., Chatterjee, S., Chakrabarty, I.: Sequential quantum secret sharing in a noisy environment aided with weak measurements. Eur. Phys. J. D 70, 114 (2016)

    ADS  Google Scholar 

  12. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    ADS  MathSciNet  MATH  Google Scholar 

  13. Horodecki, R., Horodecki, M., Horodecki, P.: Teleportation, Bell’s inequalities and inseparability. Phys. Lett. A 222, 21 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  14. Bennett, C.H., Wiesner, S.J.: Communication via one and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    ADS  MathSciNet  MATH  Google Scholar 

  15. Nepal, R., Prabhu, R., Sen De, A., Sen, U.: Maximally-dense-coding-capable quantum states. Phys. Rev. A 87, 032336 (2013)

    ADS  Google Scholar 

  16. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Bose, S., Vedral, V., Knight, P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57, 822 (1998)

    ADS  Google Scholar 

  18. Zukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.K.: “Event-ready-detectors” Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287 (1993)

    ADS  Google Scholar 

  19. Sazim, S., Chakrabarty, I.: A study of teleportation and super dense coding capacity in remote entanglement distribution. Eur. Phys. J. D 67, 174 (2013)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  21. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802 (1982)

    ADS  MATH  Google Scholar 

  22. Pati, A.K., Braunstein, S.L.: Impossibility of deleting an unknown quantum state. Nature 404, 164 (2000)

    ADS  Google Scholar 

  23. Pati, A.K., Sanders, B.C.: No-partial erasure of quantum information. Phys. Lett. A 359, 31 (2006)

    ADS  Google Scholar 

  24. Chattopadhyay, I., Choudhary, S.K., Kar, G., Kunkri, S., Sarkar, D.: No-flipping as a consequence of no-signalling and non-increase of entanglement under LOCC. Phys. Lett. A 351, 384 (2006)

    ADS  MATH  Google Scholar 

  25. Chakrabarty, I.: Impossibility of partial swapping of quantum information. Int. J. Quant. Inf. 5, 605 (2007)

    MATH  Google Scholar 

  26. Zhou, D.L., Zeng, B., You, L.: Quantum information cannot be split into complementary parts. Phys. Lett. A 352, 41 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  27. Oszmaniec, M., Grudka, A., Horodecki, M., Wójcik, A.: Creating a superposition of unknown quantum states. Phys. Rev. Lett. 116, 110403 (2016)

    ADS  Google Scholar 

  28. Bužek, V., Hillery, M.: Quantum copying: beyond the no cloning theorem. Phys. Rev. A 54, 1844 (1996)

    ADS  MathSciNet  Google Scholar 

  29. Gisin, N., Massar, S.: Optimal quantum cloning machines. Phys. Rev. Lett. 79, 2153 (1997)

    ADS  Google Scholar 

  30. Bužek, V., Hillery, M.: Universal optimal cloning of arbitrary quantum states: from qubits to quantum registers. Phys. Rev. Lett. 81, 5003 (1998)

    ADS  Google Scholar 

  31. Bruß, D., DiVincenzo, D.P., Ekert, A., Fuchs, C.A., Macchiavello, C., Smolin, J.A.: Optimal universal and state dependent quantum cloning. Phys. Rev. A 57, 2368 (1998)

    ADS  Google Scholar 

  32. Cerf, N.J.: Pauli cloning of a quantum bit. Phys. Rev. Lett. 84, 4497 (2000)

    ADS  Google Scholar 

  33. Cerf, N.J.: Asymmetric quantum cloning machines in any dimension. J. Mod. Opt. 47, 187 (2000)

    ADS  Google Scholar 

  34. Scarani, V., Iblisdir, S., Gisin, N., Acin, A.: Quantum cloning. Rev. Mod. Phys. 77, 1225 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  35. Adhikari, S., Choudhury, B.S., Chakrabarty, I.: Broadcasting of inseparability. J. Phys. A 39, 8439 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  36. Wang, M.-H., Cai, Q.-Y.: High-fidelity quantum cloning of two non orthogonal quantum states via weak measurements. Phys. Rev. A 99, 012324 (2019)

    ADS  Google Scholar 

  37. Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)

    ADS  Google Scholar 

  38. Ghiu, I.: Asymmetric quantum telecloning of d-level systems and broadcasting of entanglement to different locations using the “many-to-many” communication protocol. Phys. Rev. A 67, 012323 (2003)

    ADS  Google Scholar 

  39. Gruska, J.: Quantum entanglement as a new information processing resource. New Gener. Comput. 21, 279 (2003)

    MATH  Google Scholar 

  40. Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

    ADS  MATH  Google Scholar 

  41. White, A.G., James, D.F., Eberhard, P.H., Kwiat, P.G.: Non maximally entangled states: production, characterization, and utilization. Phys. Rev. Lett. 83, 3103 (1999)

    ADS  Google Scholar 

  42. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    ADS  Google Scholar 

  43. Murao, M., Plenio, M.B., Popescu, S., Vedral, V., Knight, P.L.: Multiparticle entanglement purification protocols. Phys. Rev. A 57, R4075 (1998)

    ADS  Google Scholar 

  44. Jain, A., Chakrabarty, I., Chatterjee, S.: Asymmetric broadcasting of entanglement and correlations. Phys. Rev. A 99, 022315 (2019)

    ADS  Google Scholar 

  45. Bužek, V., Vedral, V., Plenio, M.B., Knight, P.L., Hillery, M.: Broadcasting of entanglement via local copying. Phys. Rev. A 55, 3327 (1997)

    ADS  MathSciNet  Google Scholar 

  46. Bandyopadhyay, S., Kar, G.: Broadcasting of entanglement and universal quantum cloners. Phys. Rev. A 60, 3296 (1999)

    ADS  Google Scholar 

  47. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. General 34, 6899 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  48. Chatterjee, S., Sazim, S., Chakrabarty, I.: Broadcasting of quantum correlations: possibilities and impossibilities. Phys. Rev. A 93, 042309 (2016)

    ADS  Google Scholar 

  49. Lang, M.D., Caves, C.M.: Quantum discord and the geometry of Bell-diagonal states. Phys. Rev. Lett. 105, 150501 (2010)

    ADS  Google Scholar 

  50. Bužek, V., Hillery, M.: Universal optimal cloning of qubits and quantum registers. In: Quantum Computing and Quantum Communications. Springer, pp. 235–246 (1999)

  51. Sharma, U.K., Chakrabarty, I., Shukla, M.K.: Broadcasting quantum coherence via cloning. Phys. Rev. A 96, 052319 (2017)

    Google Scholar 

  52. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  53. Horodecki, M.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  54. Chitambar, E., Leung, D., Mancinska, L., Ozols, M., Winter, A.: Everything you always wanted to know about LOCC (but were afraid to ask). Commun. Math. Phys. 328, 303 (2014)

    ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

S.C. thanks Prof. Mark M. Wilde for his insightful suggestions. S.C. acknowledges the internship grant from Erlangen Graduate School in Advanced Optical Technologies (SAOT) for supporting the research work as an intern at IIIT, Hyderabad and HRI, Allahabad, India.

Author information

Author notes

  1. Sourav Chatterjee

    Present address: Raman Research Institute, Sadashivanagar, Bangalore, Karnataka, 560080, India

Authors and Affiliations

  1. Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana, 500032, India

    Manish Kumar Shukla & Sourav Chatterjee

  2. Center for Security, Theory and Algorithmic Research, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana, 500032, India

    Indranil Chakrabarty

  3. SAOT, Erlangen Graduate School in Advanced Optical Technologies, Paul-Gordan-Strasse 6, 91052, Erlangen, Germany

    Sourav Chatterjee

Authors
  1. Manish Kumar Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Indranil Chakrabarty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sourav Chatterjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sourav Chatterjee.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shukla, M.K., Chakrabarty, I. & Chatterjee, S. Broadcasting of entanglement via orthogonal and non-orthogonal state-dependent cloners. Quantum Inf Process 19, 15 (2020). https://doi.org/10.1007/s11128-019-2500-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2500-6

Keywords

Search

Navigation