LPTMS PhD Proposal: Entanglement and tensor representation of quantum states
Responsable:Olivier GIRAUD 0169153175
Quantum information processing holds large promises for increased computational power, communication possibilities, and metrology. A major part of the theoretical research in the field has focused on identifying, quantifying, and understanding the quantum resources that enable such enhancements. Most prominent is the research on entanglement, which was identified as key resource early on: bipartite entanglement is by now well understood, and research efforts focus on multipartite entanglement, where the situation is much richer - and much more complicated.
Understanding or classifying multipartite entanglement for generic quantum states is of course a daunting task. For states symmetric under exchange of particles, one may hope to make progress due to the drastically reduced Hilbert-space dimension. In the case of symmetric states, we have developed a theory of “quantumness” and “classicality”, based on coherent states, which can be reformulated in terms of multipartite entanglement [1,2]. However, the general characterization of quantumness and classicality remains an open question.
The starting point for this internship will be a recently developed tensorial picture of symmetric states, that generalizes the Bloch sphere picture of a two-level system . Many applications open up. Remarkably, this picture allows to map questions about entanglement onto mathematically well-studied problems. As a primary goal, we will exploit this existing mathematical knowledge to obtain more powerful means of identifying entangled symmetric states. The internship may be followed by a thesis. Depending on the taste and background of the student, more mathematically oriented topics (representation theory, generalized coherent states) or more physical aspects (metrology, quantum channels) could be considered.
 O. Giraud, P. Braun and D. Braun, Classicality of spin states, Phys. Rev. A 78, 042112 (2008).
 O. Giraud, P. Braun, and D. Braun, Quantifying Quantumness and the Quest for Queens of Quantum, New J. Phys. 12, 063005 (2010).
 O. Giraud et al., Tensor Representation of Spin States, Phys. Rev. Lett. 114, 80401 (2015).
 D. Baguette, F. Damanet, O. Giraud, and J. Martin, Anticoherence of spin states with point group symmetries, Phys. Rev. A 92, 052333 (2015).