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On the reversible extraction of classical information from a quantum source

Author

Listed:
  • Barnum, H

    (Center for Mathematical Economics, Bielefeld University)

  • Hayden, P

    (Center for Mathematical Economics, Bielefeld University)

  • Jozsa, R

    (Center for Mathematical Economics, Bielefeld University)

  • Winter, A

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Consider a source epsilon of pure quantum states with von Neumann entropy S. By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits per signal (the Schumacher limit) in such a way that entire strings may be recovered with arbitrarily high fidelity. Suppose that classical storage is flee while quantum storage is expensive and suppose that the states of epsilon do not fall into two or more orthogonal subspaces. We show that if epsilon can be compressed with arbitrarily high fidelity into A qubits per signal plus any amount of auxiliary classical storage, then A must still be at least as large as the Schumacher limit S of epsilon. Thus no part of the quantum information content of epsilon can be faithfully replaced by classical information. If the states do fall into orthogonal subspaces, then A may be less than S, but only by an amount not exceeding the amount of classical information specifying the subspace for a signal from the source.

Suggested Citation

  • Barnum, H & Hayden, P & Jozsa, R & Winter, A, 2010. "On the reversible extraction of classical information from a quantum source," Center for Mathematical Economics Working Papers 457, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:457
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    References listed on IDEAS

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    Cited by:

    1. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    3. repec:gam:jgames:v:8:y:2017:i:4:p:51-:d:119855 is not listed on IDEAS
    4. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    5. Prummer, Anja & Siedlarek, Jan-Peter, 2017. "Community leaders and the preservation of cultural traits," Journal of Economic Theory, Elsevier, vol. 168(C), pages 143-176.
    6. repec:hal:cesptp:halshs-00906367 is not listed on IDEAS
    7. Anja Prummer & Jan-Peter Siedlarek, 2014. "Institutions and the Preservation of Cultural Traits," Cambridge Working Papers in Economics 1465, Faculty of Economics, University of Cambridge.
    8. Manuel Förster & Michel Grabisch & Agnieszka Rusinowska, 2012. "Ordered Weighted Averaging in Social Networks," Documents de travail du Centre d'Economie de la Sorbonne 12056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Yann Algan & Pierre Cahuc, 2010. "Inherited Trust and Growth," American Economic Review, American Economic Association, vol. 100(5), pages 2060-2092, December.
    10. Olcina, Gonzalo & Panebianco, Fabrizio & Zenou, Yves, 2017. "Conformism, Social Norms and the Dynamics of Assimilation," CEPR Discussion Papers 12166, C.E.P.R. Discussion Papers.
    11. Boyd, G & Engels, Jürgen & Karsch, Frithjof & Laermann, Edwin & Legeland, C & Lütgemeier, M & Petersson, Bengt, 2010. "Thermodynamics of SU(3) lattice gauge theory," Center for Mathematical Economics Working Papers 469, Center for Mathematical Economics, Bielefeld University.
    12. Cheung, Man-Wah & WU, JIABIN, 2016. "On The Transmission of Continuous Cultural Traits," MPRA Paper 69934, University Library of Munich, Germany.
    13. Panebianco, Fabrizio & Verdier, Thierry, 2015. "Paternalism, Cultural Transmission and Diffusion on Complex Networks," CEPR Discussion Papers 10722, C.E.P.R. Discussion Papers.
    14. Del Bello, Carlo & Panebianco, Fabrizio & Verdier, Thierry & Zenou, Yves, 2016. "Cultural Transmission and Socialization Spillovers in Education," CEPR Discussion Papers 11419, C.E.P.R. Discussion Papers.

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    Keywords

    quantum information; quantum source coding; reversible information extraction; information compression;

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