Description
Pure states of multipartite quantum systems are described by tensors, and tensor restriction corresponds to a transformation between two states by local operations and classical communication that succeeds with a nonzero probability. By an asymptotic restriction we mean a sequence of restrictions between Kronecker powers of the tensors, which corresponds to a transformation between many copies, and in principle allows an arbitrarily rapid decay of the success probability as the number of copies is increased. In the simplest case, the asymptotic restriction arises from a single-copy probabilistic transformation, which gives a simple exponential lower bound on the success probability. However, it is also possible that a tensor asymptotically restricts to another while there is no restriction between their nth powers for any n. 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 entanglement transformations from a given degeneration and determine its success probability in the many-copy limit. Based on joint work with Dávid Bugár.