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H 1 Finite dimensional Hilbert space: spin coherent, basis coherent and anti-coherent states

Auteurs : Zyczkowski, Karol (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Among the set of all pure states living in a finite dimensional Hilbert space $\mathcal{H}_N$one distinguishes subsets of states satisfying some natural condition. One basis independent choice, consist in selecting the spin coherent states, corresponding to the $SU(2)$ group, or generalized, $SU(K)$ coherent states. Another often studied example is basis dependent, as states coherent with respect to a given basis are distinguished by the fact that the moduli of their off-diagonal elements (called 'coherences') are as large as possible. It is natural to define 'anti-coherent' states, which are maximally distant to the set of coherent states and to quantify the degree of coherence of a given state can by its distance to the set of anti-coherent states. For instance, the separable states of a system composed of two subsystems with $N$ levels are coherent with respect to the composite group $SU(N)\times SU(N)$, while in this setup, the anti-coherent states are maximally entangled.

    Codes MSC :
    46C05 - Hilbert and pre-Hilbert spaces: geometry and topology
    81R30 - Coherent states; squeezed states
    81P40 - Quantum coherence, entanglement, quantum correlations

    Informations sur la rencontre

    Nom du congrès : Coherent states and their applications: a contemporary panorama / Etats cohérents et leurs applications : un panorama contemporain
    Organisteurs Congrès : Antoine, Jean-Pierre ; Bagarello, Fabio ; Gazeau, Jean-Pierre ; Ali, Syed Twareque
    Dates : 14/11/2016 - 18/11/2016
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1461.html

    Citation Data

    DOI : 10.24350/CIRM.V.19090903
    Cite this video as: Zyczkowski, Karol (2016). Finite dimensional Hilbert space: spin coherent, basis coherent and anti-coherent states. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19090903
    URI : http://dx.doi.org/10.24350/CIRM.V.19090903


    Voir aussi

    Bibliographie

    1. Puchala, Z., Rudnicki, L., Chabuda, K., Paraniak, M., & Zyczkowski, K. (2015). Certainty relations, mutual entanglement and non-displacable manifolds. Physical Review A, 92(3), 032109 - https://doi.org/10.1103/PhysRevA.92.032109

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