Admissible transformations of quantum networks and their applications in quantum information processing

          @misc{ pirsa_PIRSA:08120039,
            doi = {10.48660/08120039},
            url = {https://pirsa.org/08120039},
            author = {Chiribella, Giulio},
            keywords = {Quantum Information},
            language = {en},
            title = {Admissible transformations of quantum networks and their applications in quantum information processing},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {dec},
            note = {PIRSA:08120039 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum operations are known to be the most general state transformations that can be applied to parts of compound systems compatibly with the probabilistic structure of quantum mechanics. What about the most general transformations of quantum operations? It turns out that any such general transformation can be realized by a quantum network with an open slot in which the input operation can be inserted, thus programming the resulting circuit. Moreover, one can recursively iterate this construction, generating an infinite hierarchy of admissible transformations and proving their realization within the circuit model of quantum mechanics. These results provide the basis of a new method to optimize quantum networks for information processing tasks, including e.g. gate estimation, discrimination, programming, and cloning. As examples of application, I will present here the optimal quantum networks for estimation of group transformations, for the alignment of reference frames with multiple communication rounds, and for universal cloning of unitary transformations.