Finite dimensional Hilbert space: spin coherent, basis coherent and anti-coherent states | Vidéo | Carmin.tv

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

By Karol Zyczkowski

Appears in collection : Coherent states and their applications: a contemporary panorama / Etats cohérents et leurs applications : un panorama contemporain

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.

Information about the video

Date of recording 17/11/2016
Date of publication 23/11/2016
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19090903
Cite this video Zyczkowski, Karol (17/11/2016). Finite dimensional Hilbert space: spin coherent, basis coherent and anti-coherent states. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19090903
URL https://dx.doi.org/10.24350/CIRM.V.19090903

Domain(s)

Quantum Physics

Bibliography

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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