6) Optics and quantum information

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Le groupe d’Optique et Information Quantique s’intéresse, d’un point de vue théorique, à l’étude des propriétés quantiques de systèmes optiques multimode dans les degrés spatiales et temporelles de la liberté et de leurs impact pour le traitement tout-optique dans le contexte de l’information, la communication et la métrologie quantiques.

Notamment, le groupe est intéressé aux limites fondamentales imposées par la nature quantique de la lumière dans le codage, la transmission et de l’extraction de l’information au moyen de faisceaux optiques multimodes. Limites qui peuvent toutefois être dépassées par la manipulation des fluctuations quantiques.

Par ailleurs, un des problèmes fondamentaux de l’information quantique est de comprendre les propriétés fondamentales de l’intrication quantique et de les exploiter pour effectuer des tâches qui sont inaccessibles aux protocoles classiques de traitement de l’information. Dans ce contexte, les systèmes fortement multimodes pourraient permettre d’implémenter des réseaux de communication quantique, des protocoles de cryptographie pour la distribution sécurisé d’une clé ou d’augmenter le débit de l’échange d’information.

Après avoir été la première à introduire les concepts de compression locale du bruit quantique et d’intrication locale, l’équipe a fait évoluer ses activités en collaboration avec l’équipe d’Information Quantique de Bruxelles dirigée par Nicolas Cerf, en s’intéressant notamment à la compréhension et la caractérisation des propriétés fondamentales de l’intrication entre plusieurs paries au moyen du formalisme des invariants symplectiques. La synthèse entre ces deux thématiques a naturellement conduit à la formulation d’une théorie de l’intrication multipartite tenant compte des degrés de liberté spatiaux. L’équipe a participé activement de 2008 à 2011 au projet européen FP7 HIDEAS, en collaboration avec d’autres groupes théoriques et expérimentaux s’intéressant également aux propriétés quantiques des systèmes multimodes.

 

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a) Multimode quantum optics

Multimode quantum optics, in general, studies the properties of quantum noise and quantum correlations in optical systems characterized by a large number of modes. An optical image is an example of multimode optical field since it can be decomposed over a basis of transverse modes (i.e. Hermite-Gauss, Laguerre-Gauss modes).

Mainly interested to optical systems with a large number of photons, also known as Continuous Variable (CV) regime, our work is focused on

  • the study of compact and scalable sources and their dynamical properties for the generation of multimode CV quantum optical states : in multimode quantum states, quantum correlations are shared and distributed among the parties, according to the source, in order to exploit the generated states for quantum tasks like teleportation, quantum key distribution or one-way quantum computation. Typical states of interest are for example Green-Horne-Zeilinger states, Werner states, cluster states.
  • the study of fundamental properties and characterization of CV quantum states : Typical sources exploiting second order non-linearities generates quantum states whose statistical distribution of noise fluctuations can be completely described by a Gaussian characteristic function. In this case all the information is contained in the covariance matrix.

We study the symplectic invariants associated to a given state in order to characterize the amount of multipartite entanglement ; in particular we are interested to the structure of multipartite correlations generated in systems such as multimode OPOs and OPAs. For those systems we proved that the scaling properties of entanglement as a function of the number N of parties considered are different and depends of the structure of the intermode coupling matrix (also known as the adjacency matrix).

We developped a generalized theory of the symplectic characterization of multimode entanglement by considering the spatial and temporal degrees of freedom of the modes involved in the entangling process. It is possible, in fact, to define in a more general way a correlation matrix, which is the generalization of the covariance matrix, by keeping into account the space and time variables. Also, for systems that are homogeneous in space and stationary in time, it is possible to define a spectral density component of correlation function in the Fourier domain depending on one space-time frequency. As a consequence every symplectic invariant can be completely generalized to the space and time degrees of freedom and the multimode entanglement results to be dependent on these variables too. Accordingly defined a temporal and a spatial dimensions that characterize the structure of multipartite entanglement. In particular we shown that such dimensions depends on the number N of modes participating to multimode entanglement.

 

2) Imagerie Quantique Temporelle

Temporal imaging is a technique that enables manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. The concept of temporal imaging uses the notion of space-time duality with dispersion phenomena playing the role of diffraction and quadratic phase modulation in time acting as a time lens.

In a regime where quantum fluctuations are negligible, the technology of temporal imaging allows for an all-optical manipulation of pulses while preserving high-speed communication. However, as for conventional spatial imaging, classical temporal imaging protocols will reach a regime where the intrinsic quantum nature of light cannot be neglected. Furthermore, in the framework of quantum communication an all-optical manipulation of the information must preserve the quantum character of the quantum states used for encoding and transmitting the information. As a consequence, a classical theory of temporal imaging is not sufficient and a formulation in the context of quantum mechanics is necessary.

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