QLunch: Péter Vrana

Speaker: Péter Vrana

Title: Error exponents from tensor degenerations

Abstract: Asymptotic tensor restriction corresponds to asymptotic entanglement transformation by stochastic local operations and classical communication, in principle allowing an arbitrarily rapid decay of the success probability as the number of copies is increased. A challenging refinement of this problem, so far completely solved only in the case of bipartite entanglement concentration, is to find the error exponent depending on the transformation rate. In the simplest case, when the asymptotic restriction arises from a single-copy probabilistic transformation, standard tail estimates for the binomial distribution imply bounds on the error exponents. Tensor degeneration is a fundamental tool for proving asymptotic restriction when no single-copy transformation is possible. In this talk, I explain the construction of a family of asymptotic LOCC transformations from a given degeneration and determine its success probability in the many-copy limit, resulting in an upper bound on the strong converse exponent. Based on joint work with Dávid Bugár.