Skip to main content
SpringerLink
Log in

Slepian–Wolf coding with quantum side information

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we consider the classical Slepian–Wolf coding with quantum side information, corresponding to the compression of two correlated classical parts, using their quantum parts as side information at the decoder. By quantum Feinstein’s lemma, we give the achievable rate region. We then extend to the multiple classical–quantum sources case. We also consider the classical Slepian–Wolf coding with full (local) quantum helper. Using the measure compression theorem, we get the achievable rate region and extend to the multiple classical–quantum sources case.

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
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Shannon, C.E.: A mathematical theory of communication. Bell. Syst. Tech. J. 27(3), 379–423 (1948)

    MathSciNet  MATH  Google Scholar 

  2. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Tsinghua University Press (2006)

    MATH  Google Scholar 

  3. Slepian, D., Wolf, J.: Noiseless coding of correlated information sources. IEEE Trans. Inf. Theory 19(4), 471–480 (1973)

    MathSciNet  MATH  Google Scholar 

  4. Wyner, A.: On source coding with side information at the decoder. IEEE Trans. Inf. Theory 21(3), 294–300 (1975)

    MathSciNet  MATH  Google Scholar 

  5. Ahlswede, R., Körner, J.: Source coding with side information and a converse for degraded broadcast channels. IEEE Trans. Inf. Theory 21(6), 629–637 (1975)

    MathSciNet  MATH  Google Scholar 

  6. Cover, T.: A proof of the data compression theorem of Slepian and Wolf for ergodic sources (Corresp.). IEEE Trans. Inf. Theory 21(2), 226–228 (1975)

    MathSciNet  MATH  ADS  Google Scholar 

  7. Gamal, A.E., Kim, Y.H.: Network Information Theory. Cambridge University Press (2011)

    MATH  Google Scholar 

  8. Nomura, R., Han, T.S.: Second-order Slepian–Wolf coding theorems for non-mixed and mixed sources. IEEE Trans. Inf. Theory 60(9), 5553–5572 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Watanabe, S., Kuzuoka, S., Tan, V.Y.F.: Nonasymptotic and second-order achievability bounds for coding with side-information. IEEE Trans. Inf. Theory 61(4), 1574–1605 (2015)

    MathSciNet  MATH  Google Scholar 

  10. Yagi, H., Han, T.S., Nomura, R.: First- and second-order coding theorems for mixed memoryless channels with general mixture. IEEE Trans. Inf. Theory 62(8), 4395–4412 (2016)

    MathSciNet  MATH  Google Scholar 

  11. Sakai, Y., Tan, V.Y.F.: Variable-length source dispersions differ under maximum and average error criteria. IEEE Trans. Inf. Theory 66(12), 7565–7587 (2020)

    MathSciNet  MATH  Google Scholar 

  12. Averbuch R.T., Merhav N.: Trade-offs between error and excess-rate exponents of typical Slepian–Wolf codes. In: IEEE International Symposium on Information Theory (ISIT), pp. 924–929 (2021)

  13. Lu, J., Xu, Y., Zhang, P., Wang, Q.: On secure one-helper source coding with action-dependent side information. IEEE Trans. Inf. Theory 67(1), 95–110 (2021)

    MathSciNet  MATH  Google Scholar 

  14. Liu, J.: Dispersion bound for the Wyner–Ahlswede–Körner network via a semigroup method on types. IEEE Trans. Inf. Theory 67(2), 869–885 (2021)

    MATH  Google Scholar 

  15. Takeuchi D., Watanabe S.: The achievable rate region of Wyner–Ahlswede–Körner coding problem for mixed sources. In: IEEE Information Theory Workshop (ITW), pp. 1–6 (2021)

  16. Tang, R., Xie, S., Wu, Y.: On the achievable rate region of the k-receiver broadcast channels via exhaustive message splitting. Entropy 23(11), 1408 (2021)

    MathSciNet  ADS  Google Scholar 

  17. Salehkalaibar, S., Wigger, M.: Distributed hypothesis testing over noisy broadcast channels. Information 12(7), 268 (2021)

    Google Scholar 

  18. Vatedka S., Chandar V., Tchamkerten A.: Locally decodable Slepian–Wolf compression. In: IEEE International Symposium on Information Theory (ISIT), pp. 1430–1435 (2022)

  19. Vatedka S., Chandar V., Tchamkerten A.: Local decoding in distributed compression. IEEE Journal on Selected Areas in Information Theory (JSAIT) (2023)

  20. Srinadh, V., Rao, M.S., Sahoo, M.R., et al.: An analytical study on security and future research of internet of things. Mater. Today Proc. (2021)

  21. Tariq, F., Khandaker, M.R.A., Wong, K.K., et al.: A speculative study on 6G. IEEE Wirel. Commun. 27, 118–125 (2020)

    Google Scholar 

  22. Wang, C., Rahman, A.: Quantum-enabled 6G wireless networks: opportunities and challenges. IEEE Wirel. Commun. 29, 58–69 (2022)

    Google Scholar 

  23. Urgelles H., Picazo-Martinez P., Monserrat J.F.: Application of quantum computing to accurate positioning in 6G indoor scenarios. In: IEEE International Conference on Communications, pp. 643–647 (2022)

  24. Vlachos E., Blekos K.: Quantum computing-assisted channel estimation for massive MIMO mmWave systems. In: IEEE International Conference on Very Large Scale Integration (VLSI-SoC), pp. 1–6 (2022)

  25. Zaman, F., Farooq, A., et al.: Quantum Machine Intelligence for 6G URLLC. IEEE Wirel. Commun. 30, 22–30 (2023)

    Google Scholar 

  26. Holevo, A.S.: The capacity of the quantum channel with general signal states. IEEE Trans. Inf. Theory 44(1), 269–273 (1998)

    MathSciNet  MATH  Google Scholar 

  27. Schumacher, B.: Quantum coding. Phys. Rev. A 51(4), 2738–2747 (1995)

    MathSciNet  ADS  Google Scholar 

  28. Horodecki, M., Oppenheim, J.: Partial quantum information. Nature 436, 673–676 (2005)

    ADS  Google Scholar 

  29. Horodecki, M., Oppenheim, J., Winter, A.: Quantum state merging and negative information. Commun. Math. Phys. 269(1), 107–136 (2006)

    MathSciNet  MATH  ADS  Google Scholar 

  30. Abeyesinghe, A., Devetak, I., Hayden, P., Winter, A.: The mother of all protocols: restructuring quantum information’s family tree. Proc. R. Soc. A. 465, 2537–2563 (2009)

    MathSciNet  MATH  ADS  Google Scholar 

  31. Anshu, A., Jain, R., Warsi, N.A.: A generalized quantum Slepian–Wolf. IEEE Trans. Inf. Theory 64(3), 1436–1453 (2018)

    MathSciNet  MATH  Google Scholar 

  32. Devetak, I., Winter, A.: Classical data compression with quantum side information. Phys. Rev. A 68(4), 042301 (2003)

    ADS  Google Scholar 

  33. Khanian, Z.B., Winter, A.: Distributed compression of correlated classical quantum sources or: the price of ignorance. IEEE Trans. Inf. Theory 66(9), 5620–5633 (2020)

    MathSciNet  MATH  Google Scholar 

  34. Yard, J.T., Devetak, I.: Optimal quantum source coding with quantum side information at the encoder and decoder. IEEE Trans. Inf. Theory 55(11), 5339–5351 (2009)

    MathSciNet  MATH  Google Scholar 

  35. Hsieh, M.-H., Watanabe, S.: Channel simulation and coded source compression. IEEE Trans. Inf. Theory 62(11), 6609–6619 (2016)

    MathSciNet  MATH  Google Scholar 

  36. Anshu, A., Yao, P.: On the compression of messages in the multi-party setting. IEEE Trans. Inf. Theory 66, 2091–2114 (2020)

    MathSciNet  MATH  Google Scholar 

  37. Pereg, U., Deppe, C., Boche, H.: Quantum channel state masking. IEEE Trans. Inf. Theory 67(4), 2245–2268 (2021)

    MathSciNet  MATH  Google Scholar 

  38. Pereg, U., Deppe, C., Boche, H.: Classical state masking over a quantum channel. Phys. Rev. A 105(2), 022442 (2022)

    MathSciNet  ADS  Google Scholar 

  39. Sohail M.A., Anwar A.T., Pradhan S.S.: Unified approach for computing sum of sources over CQ-MAC. In: IEEE International Symposium on Information Theory (ISIT), pp. 1868–1873 (2022)

  40. Chou, R.A.: Private classical communication over quantum multiple-access channels. IEEE Trans. Inf. Theory 68(3), 1782–1794 (2022)

    MathSciNet  MATH  Google Scholar 

  41. Zhou, C., Wang, X., Zhang, Z., et al.: Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes. Sci. China Phys. Mech. Astron. 64, 260311 (2021)

    ADS  Google Scholar 

  42. Fan, H.: Efficient implementation of quantum arithmetic operation circuits. Sci. China Phys. Mech. Astron. 64, 210332 (2021)

    ADS  Google Scholar 

  43. Yan, P.S., Zhou, L., Zhong, W., et al.: Advances in quantum entanglement purification. Sci. China Phys. Mech. Astron. 66, 250301 (2023)

    ADS  Google Scholar 

  44. Sheng, Y.B., Zhou, L.: Accessible technology enables practical quantum secret sharing. Sci. China Phys. Mech. Astron. 66, 260331 (2023)

    ADS  Google Scholar 

  45. Datta, N., Hsieh, M.H.: The apex of the family tree of protocols: optimal rates and resource inequalities. New J. Phys. 13(9), 093042 (2011)

    MATH  ADS  Google Scholar 

  46. Renes, J.M., Renner, R.: One-shot classical data compression with quantum side information and the distillation of common randomness or secret keys. IEEE Trans. Inf. Theory 58(3), 1985–1991 (2012)

    MathSciNet  MATH  Google Scholar 

  47. Datta, N., Renes, J.M., Renner, R., Wilde, M.M.: One-shot lossy quantum data compression. IEEE Trans. Inf. Theory 59(12), 8057–8076 (2013)

    MathSciNet  MATH  Google Scholar 

  48. Watanabe S., Kuzuoka S., Tan V.Y.F.: Non-asymptotic and second-order achievability bounds for source coding with side-information. In: IEEE International Symposium on Information Theory (ISIT) (2013)

  49. Cheng, H.C., Hanson, E.P., Datta, N., Hsieh, M.H.: Non-asymptotic classical data compression with quantum side information. IEEE Trans. Inf. Theory 67(2), 902–930 (2021)

    MathSciNet  MATH  Google Scholar 

  50. Cheng, H.C., Hanson, E.P., Datta, N., Hsieh, M.H.: Duality between source coding with quantum side information and classical-quantum channel coding. IEEE Trans. Inf. Theory 68(11), 7315–7345 (2022)

    MathSciNet  Google Scholar 

  51. Wakakuwa, E., Nakata, Y., Hsieh, M.H.: One-shot hybrid state redistribution. Quantum 6, 724 (2022)

    Google Scholar 

  52. Parthasarathy K.R.: Coding theorems of classical and quantum information theory. Hindustan Book Agency (2013)

  53. Winter A.: Coding Theorems of Quantum Information Theory (1999)

  54. Datta N., Dorlas T.: A quantum version of Feinstein’s theorem and its application to channel coding. In: IEEE International Symposium on Information Theory (ISIT), pp. 441–445 (2006)

  55. Winter, A.: ‘Extrinsic’ and ‘intrinsic’ data in quantum measurements: asymptotic convex decomposition of positive operator valued measures. Commun. Math. Phys. 244(1), 157–185 (2004)

    MathSciNet  MATH  ADS  Google Scholar 

  56. Wilde, M.M., Hayden, P., Buscemi, F., Hsieh, M.H.: The information-theoretic costs of simulating quantum measurements. J. Phys. A 45(45), 453001 (2012)

    MathSciNet  MATH  Google Scholar 

  57. Nielsen M.A., Chuang I.L.: Quantum computation and quantum information. 10th anniversary ed. Cambridge University Press (2010)

  58. Wyner, A., Ziv, J.: The rate-distortion function for source coding with side information at the decoder. IEEE Trans. Inf. Theory 22(1), 1–10 (1976)

    MathSciNet  MATH  Google Scholar 

  59. Datta, N., Hsieh, M.H., Wilde, M.M.: Quantum rate distortion, reverse Shannon theorems, and source-channel separation. IEEE Trans. Inf. Theory 59(1), 615–630 (2013)

    MathSciNet  MATH  Google Scholar 

  60. Wilde, M.M., Datta, N., Hsieh, M.H., Winter, A.: Quantum rate-distortion coding with auxiliary resources. IEEE Trans. Inf. Theory 59(10), 6755–6773 (2013)

    MathSciNet  MATH  Google Scholar 

  61. Khanian Z.B., Winter A.: A rate-distortion perspective on quantum state redistribution. Preprint at arXiv:2112.11952 (2021)

Download references

Acknowledgements

Z. X. was supported by the National Natural Science Foundation of China (No. 61671280) and by the Funded Projects for the Academic Leaders and Academic Backbones, Shaanxi Normal University (No. 16QNGG013). H. F. was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and Beijing Natural Science Foundation (Grant No. Z200009).

Author information

Authors and Affiliations

  1. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Xiaomin Liu & Zhengjun Xi

  2. Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Heng Fan

  3. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China

    Heng Fan

  4. Beijing Academy of Quantum Information Sciences, Beijing, 100193, China

    Heng Fan

Authors
  1. Xiaomin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengjun Xi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heng Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Zhengjun Xi or Heng Fan.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Xi, Z. & Fan, H. Slepian–Wolf coding with quantum side information. Quantum Inf Process 22, 407 (2023). https://doi.org/10.1007/s11128-023-04153-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04153-4

Keywords

Search

Navigation