Leírás
The trade-off relation between the rate and the strong
converse exponent for probabilistic asymptotic entanglement
transformations between pure multipartite states can in principle be
characterised in terms of a class of entanglement measures determined
implicitly by a set of strong axioms. A nontrivial family of such
functionals has recently been constructed, but their previously known
characterisations have so far only made it possible to evaluate them in
very simple cases. In this paper we derive a new regularised formula for
these functionals in terms of a subadditive upper bound, complementing
the previously known superadditive lower bound. The upper and lower
bounds evaluated on tensor powers differ by a logarithmically bounded
term, which provides a bound on the convergence rate. In addition, we
find that on states satisfying a certain sparsity constraint, the upper
bound is equal to the value of the corresponding additive entanglement
measure, therefore the regularisation is not needed for such states, and
the evaluation is possible via a single-letter formula. Our results
provide explicit bounds on the success probability of transformations by
local operations and classical communication and, due to the additivity
of the entanglement measures, also on the strong converse exponent for
asymptotic transformations.