Uncertainty, entropy and non-Gaussianity for mixed states

Aikaterini Mandilara, Evgueni Karpov, Nicolas J. Cerf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In the space of mixed states the Schrödinger-Robertson uncertainty relation holds though it can never be saturated. Two tight extensions of this relation in the space of mixed states exist; one proposed by Dodonov and Man'ko, where the lower limit on the uncertainty depends on the purity of the state, and another where the uncertainty is bounded by the von Neumann entropy of the state proposed by Bastiaans. Driven by the needs that have emerged in the field of quantum information, in a recent work we have extended the purity-bounded uncertainty relation by adding an additional parameter characterizing the state, namely its degree of non-Gaussianity. In this work we alternatively present a extension of the entropy-bounded uncertainty relation. The common points and differences between the two extensions of the uncertainty relation help us to draw more general conclusions concerning the bounds on the non-Gaussianity of mixed states.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Volume7727
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventQuantum Optics - Brussels, Belgium
Duration: Apr 13 2010Apr 14 2010

Other

OtherQuantum Optics
CountryBelgium
CityBrussels
Period4/13/104/14/10

Fingerprint

Uncertainty Relation
Mixed State
Entropy
entropy
Uncertainty
purity
Quantum Information

Keywords

  • Mixed states
  • Non-Gaussian states
  • Uncertainty principle

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Mandilara, A., Karpov, E., & Cerf, N. J. (2010). Uncertainty, entropy and non-Gaussianity for mixed states. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7727). [77270H] https://doi.org/10.1117/12.854750

Uncertainty, entropy and non-Gaussianity for mixed states. / Mandilara, Aikaterini; Karpov, Evgueni; Cerf, Nicolas J.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7727 2010. 77270H.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mandilara, A, Karpov, E & Cerf, NJ 2010, Uncertainty, entropy and non-Gaussianity for mixed states. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7727, 77270H, Quantum Optics, Brussels, Belgium, 4/13/10. https://doi.org/10.1117/12.854750
Mandilara A, Karpov E, Cerf NJ. Uncertainty, entropy and non-Gaussianity for mixed states. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7727. 2010. 77270H https://doi.org/10.1117/12.854750
Mandilara, Aikaterini ; Karpov, Evgueni ; Cerf, Nicolas J. / Uncertainty, entropy and non-Gaussianity for mixed states. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7727 2010.
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