Random graph states and area laws

          @misc{ pirsa_PIRSA:10070013,
            doi = {10.48660/10070013},
            url = {https://pirsa.org/10070013},
            author = {},
            keywords = {},
            language = {en},
            title = {Random graph states and area laws},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {jul},
            note = {PIRSA:10070013 see, \url{https://pirsa.org}}
          }
          

Abstract

We associate to any unoriented graph a random pure quantum state, obtained by randomly rotating a tensor product of Bell states. Marginals of such states define new ensembles of density matrices, which we study in the asymptotical regime of large Hilbert spaces. Limit eigenvalue distributions are computed, as well as average von Neumann entropies and purities. Fuss-Catalan distributions are identified as limits of the eigenvalue distributions of particular marginals. Finally, we discuss area laws for these random states. This is joint work with Benoit Collins and Karol Zyczkowski.