PIRSA:08080035

Optimal linear tomography of quantum states and processes with tight POVMs

Scott, A. (2008). Optimal linear tomography of quantum states and processes with tight POVMs. Perimeter Institute. https://pirsa.org/08080035

Scott, Andrew. Optimal linear tomography of quantum states and processes with tight POVMs. Perimeter Institute, Aug. 25, 2008, https://pirsa.org/08080035 

          @misc{ pirsa_PIRSA:08080035,
            doi = {10.48660/08080035},
            url = {https://pirsa.org/08080035},
            author = {Scott, Andrew},
            keywords = {},
            language = {en},
            title = {Optimal linear tomography of quantum states and processes with tight POVMs},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {aug},
            note = {PIRSA:08080035 see, \url{https://pirsa.org}}
          }

Andrew Scott Griffith University

DOI 10.48660/08080035
Collection
Talk Type Conference

Abstract

We introduce the concept of tight POVMs. In analogy with tight frames, these are POVMs that are as close as possible to orthonormal bases for the space they span. We show that tight rank-one POVMs define the exact class of optimal measurements for linear tomography of quantum states. In this setting they are equivalent to complex projective 2-designs. We also show that tight POVMs define the optimal class of measurements on the probe state for ancilla-assisted process tomography of unital channels. In this setting they are equivalent to unitary 2-designs.