Skip to main content
SpringerLink
Log in

Quantum Theory is an Information Theory

The Operational Framework and the Axioms

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

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

Similar content being viewed by others

Notes

  1. There is no loss of generality in this assumption, as we can always augment \(\mathsf {St}(\mathrm {A})\) and \(\mathsf {Eff}(\mathrm {A})\) to their convex hulls. However, there are exceptional cases where it may be convenient not to do so, e.g. when one considers deterministic theories, where probabilities are bound to the values 0 and 1.

References

  1. Barrett, J.: Information processing in generalized probabilistic theories. Phys. Rev. A 75, 032304 (2007)

    Article  ADS  Google Scholar 

  2. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, Part 1(0), 7–11 (2014). Theoretical aspects of quantum cryptography—celebrating 30 years of BB84

    Article  MathSciNet  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crepeau, 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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Chiribella, G., D’Ariano, G.M., Perinotti, P.: Probabilistic theories with purification. Phys. Rev. A 81, 062348 (2010)

    Article  ADS  Google Scholar 

  5. Chiribella, G., D’Ariano, G.M., Perinotti, P.: Informational derivation of quantum theory. Phys. Rev. A 84, 012311–012350 (2011)

    Article  ADS  Google Scholar 

  6. D’ Ariano, G.M.: On the missing axiom of quantum mechanics. AIP Conf. Proc. 810(1), 114–130 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  7. Fuchs, C.A.: Quantum mechanics as quantum information (and only a little more). http://arxiv.org/abs/quant-ph/0205039

  8. Hardy, L.: Quantum theory from five reasonable axioms. http://arxiv.org/abs/quant-ph/0101012

  9. Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Yuen, H.P.: Amplification of quantum states and noiseless photon amplifiers. Phys. Lett. A 113, 405 (1986)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work has been supported in part by the Templeton Foundation under the Project ID# 43796 A Quantum-Digital Universe.

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università degli Studi di Pavia, Pavia, Italy

    Giacomo M. D’Ariano & Paolo Perinotti

Authors
  1. Giacomo M. D’Ariano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Perinotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giacomo M. D’Ariano.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

D’Ariano, G.M., Perinotti, P. Quantum Theory is an Information Theory. Found Phys 46, 269–281 (2016). https://doi.org/10.1007/s10701-015-9935-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-015-9935-0

Keywords

Search

Navigation