PIRSA:10070020

Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration

Brandao, F. (2010). Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. Perimeter Institute. https://pirsa.org/10070020

Brandao, Fernando. Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. Perimeter Institute, Jul. 06, 2010, https://pirsa.org/10070020 

          @misc{ pirsa_PIRSA:10070020,
            doi = {10.48660/10070020},
            url = {https://pirsa.org/10070020},
            author = {Brandao, Fernando},
            keywords = {},
            language = {en},
            title = {Hasting{\textquoteright}s counterexamples on the minimum output entropy additivity conjecture by measure concentration},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {jul},
            note = {PIRSA:10070020 see, \url{https://pirsa.org}}
          }

Fernando Brandao California Institute of Technology (Caltech)

DOI 10.48660/10070020
Collection
Talk Type Conference

Abstract

In 2008 Hastings reported a randomized construction of channels violating the minimum output entropy additivity conjecture. In this talk we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. We prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension.