Efficient tomography of generalized coherent states

          @misc{ pirsa_PIRSA:08080054,
            doi = {10.48660/08080054},
            url = {https://pirsa.org/08080054},
            author = {Somma, Rolando},
            keywords = {},
            language = {en},
            title = {Efficient tomography of generalized coherent states},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {aug},
            note = {PIRSA:08080054 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum tomography and fidelity estimation of multi-partite systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the corresponding experimental setup. In this talk I could explain an efficient way (i.e., in polylog(d) time, with d the dimension of the Hilbert space) to perform tomography and estimate the fidelity of generalized coherent state (GCS) preparation. GCSs differ from the well known coherent states in that the associated Hilbert space is finite dimensional. In particular, the class of GCSs is very important in condensed matter applications. These results are useful to experimentalists seeking the simulations of some quantum systems, such as the Ising model in a transverse field. I\'d prefer to give a 30\' + talk late in the week, maybe on Thursday afternoon. Part of this work has been done in collaboration with ion-trap experimentalists J. Chiaverini and D. Berkeland, at Los Alamos National Laboratory. Rolando Somma.