Quantum Reference Frames and the Classification of Rotationally-Invariant Maps

          @misc{ pirsa_PIRSA:07100033,
            doi = {10.48660/07100033},
            url = {https://pirsa.org/07100033},
            author = {Boileau, Jean Christian},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum Reference Frames and the Classification of Rotationally-Invariant Maps},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {oct},
            note = {PIRSA:07100033 see, \url{https://pirsa.org}}
          }
          

Abstract

We give a convenient representation for any map which is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations. We introduce the moments of a quantum reference frame, which serve as a complete description of its properties as a frame, and investigate how many times a quantum directional reference frame represented by a spin-j system can be used to perform a certain quantum operation with a given probability of success. We provide a considerable generalization of previous results on degradation of reference frame, from which follows a classification of the dynamics of spin-j system under the repeated action of any covariant map with respect to SU(2). Joint work with Lana Sheridan, Martin Laforest and Stephen Bartlett