Skip to main content
SpringerLink
Log in

New uncertainty relations for tomographic entropy: application to squeezed states and solitons

  • Solid and Condensed State Physics
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

Using the tomographic probability distribution (symplectic tomogram) describing the quantum state (instead of the wave function or density matrix) and properties of recently introduced tomographic entropy associated with the probability distribution, the new uncertainty relation for the tomographic entropy is obtained. Examples of the entropic uncertainty relation for squeezed states and solitons of the Bose-Einstein condensate are considered.

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

Similar content being viewed by others

References

  • W. Heisenberg, Z. Phys. 43, 172 (1927)

    Article  MATH  Google Scholar 

  • E. H. Kennard, Z. Phys. 44, 326 (1927)

    Article  MATH  Google Scholar 

  • H. P. Robertson, Phys. Rev. 34, 163 (1929); 35, 667 (1930)

    Article  ADS  Google Scholar 

  • E. Schrödinger, Ber. Kgl. Akad. Wiss., Berlin 24; 296 (1930); Naturwissenschaften 23, 807; 823; 844 (1935)

    Article  Google Scholar 

  • V.V. Dodonov, E.V. Kurmyshev, V.I. Man'ko, Phys. Lett. A 79, 150 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  • E.C.G. Sudarshan, Charles B. Chiu, G. Bhamathi, Phys. Rev. 52, 43 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  • V.V. Dodonov, V.I. Man'ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the Lebedev Physical Institute (Nauka, Moscow, 1987), Vol. 183 [translated by Nova Science, New York, 1989]

  • D.A. Trifonov, J. Phys. A: Math. Gen. 33, L299 (2000); 34, L75 (2001); D.A. Trifonov, World of Physics 24, 107 (2001); D.A. Trifonov, J. Opt. Soc. Am. A 17, 2486 (2000)

    Google Scholar 

  • H.P. Robertson, Phys. Rev. 46, 794 (1934)

    Article  MATH  ADS  Google Scholar 

  • M. Karelin, J. Phys. A: Math. Gen. 38, 6393 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  • V.V. Dodonov, J. Opt. B: Quantum Semiclass. Opt. 4, R1 (2002)

  • M. Ozawa, J. Opt. B: Quantum Semiclass. Opt. 7, S672 (2005)

  • C.E. Shannon, Bell Tech. J. 27, 379 (1948)

    MathSciNet  Google Scholar 

  • I. Bialynicki-Birula, Phys. Lett. A 108, 384 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  • I.I. Hirshman, Amer. J. Math. 79, 152 (1957)

    Article  MathSciNet  Google Scholar 

  • S. Mancini, V.I. Man'ko, P. Tombesi, Phys. Lett. A 213, 1 (1996); Found. Phys. 27, 801 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • G.M. D'Ariano, S. Mancini, V.I. Man'ko, P. Tombesi, Quantum Semiclass. Opt. 8, 1017 (1996)

    Article  ADS  Google Scholar 

  • O. V. Man'ko, V.I. Man'ko, J. Russ. Laser Res. 18, 407 (1997)

    Google Scholar 

  • M.A. Man'ko, J. Russ. Laser Res. 22, 168 (2001)

    Article  Google Scholar 

  • S. De Nicola, R. Fedele, M.A. Man'ko, V.I. Man'ko, Eur. Phys. J. B 36, 385 (2003)

    Article  ADS  Google Scholar 

  • M.A. Man'ko, V.I. Man'ko, R. Vilela Mendes, A probabilistic operator symbol framework for quantum information, Los Alamos, arXiv:quant-ph/0602189 (2006); J. Phys. A: Math. Gen. (2006, in press)

  • V.V. Dodonov, V.I. Man'ko, Phys. Lett. A 239, 335 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  • V.I. Man'ko, O.V. Man'ko, Zh. Éksp. Teor. Fiz. 112, 796 (1997) [JETP, 85, 430 (1997)]

    MathSciNet  Google Scholar 

  • O.V. Man'ko, V.I. Man'ko, J. Russ. Laser Res. 25, 115 (2004)

    Article  Google Scholar 

  • S. Mancini, V. I. Man'ko, P. Tombesi, Quantum Semiclass. Opt. 7, 615 (1995)

    Article  ADS  Google Scholar 

  • O.V. Man'ko, V.I. Man'ko, G. Marmo, Phys. Scr. 62, 446 (2000); J. Phys. A: Math. Gen. 35, 699 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  • V.I. Man'ko, R.V. Mendes, Phys. Lett. A 263, 53 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • E.P. Wigner, Phys. Rev. 40, 749 (1932); E.P. Wigner, Perspectives in Quantum Theory, edited by W. Yourgrau, A. van der Merwe, Dover (New York, 1979); J. Ville, Cables et Transmission 2, 61 (1948)

    Article  MATH  ADS  Google Scholar 

  • J. Bertrand, P. Bertrand, Found. Phys. 17, 397 (1987)

    Article  MathSciNet  Google Scholar 

  • K. Vogel, H. Risken, Phys. Rev. A 40, 2847 (1989)

    Article  ADS  Google Scholar 

  • M.A. Man'ko, M.A. Man'ko, J. Russ. Laser Res. 20, 225 (1999); J. Russ. Laser Res. 21, 411 (2000)

    Google Scholar 

  • S. De Nicola, R. Fedele, M.A. Man'ko, V.I. Man'ko, J. Opt. B: Quantum Semiclass. Opt. 5, 95 (2003)

    Article  ADS  Google Scholar 

  • E.P. Gross, Nuovo Cim. 20, 454 (1961); L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)

    MATH  Google Scholar 

  • S. De Nicola, R. Fedele, M.A. Man'ko, V.I. Man'ko, in Proceedings of International Workshop `Nonlinear Physics: Theory and Experiment. II' (Gallipoli, Lecce, Italy, June–July 2002), edited by M. Ablowitz, M. Boiti, F. Pempinelli, B. Prinari (World Scientific, Singapore 2003), p. 372; J. Russ. Laser Res. 25, 1 (2004); in Symmetries in Science XI, edited by B.J. Gruber, G. Marmo, N. Yoshinaga (Kluwer Academic Publishers, London, 2004), p. 175.

    Article  MathSciNet  Google Scholar 

  • M.A. Man'ko, S. De Nicola, R. Fedele, V.I. Man'ko, in Group Theoretical Methods in Physics, Proceedings of the XXV International Colloquium on Group Theoretical Methods in Physics (Cocoyoc, Mexico, 2–6 August 2004), edited by G.S. Pogosyan, L.E. Vicent, K.-B. Wolf (Institute of Physics Publishers, Bristol, 2005), Conf. Ser. 185, p. 385

Download references

Author information

Authors and Affiliations

  1. Istituto di Cibernetica “Eduardo Caianiello” del CNR Comprensorio “A. Olivetti” Fabbr. 70, Via Campi Flegrei, 34, I-80078, Pozzuoli (NA), Italy

    S. De Nicola

  2. Dipartimento di Scienze Fisiche, Università Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, via Cintia, 80126, Napoli, Italy

    R. Fedele

  3. P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow, 119991, Russia

    M. A. Man'ko & V. I. Man'ko

Authors
  1. S. De Nicola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Fedele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Man'ko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. I. Man'ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. De Nicola.

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Nicola, S., Fedele, R., Man'ko, M. et al. New uncertainty relations for tomographic entropy: application to squeezed states and solitons. Eur. Phys. J. B 52, 191–198 (2006). https://doi.org/10.1140/epjb/e2006-00280-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2006-00280-0

PACS.

Search

Navigation