On the distillability problem of two-copy 4 × 4 Werner states: matrices A, B of at most four nonzero entries

In entanglement theory, the long-standing distillability problem asks whether the two-copy 4 × 4 Werner states are distillable under local operations and classical communications. We report the partial solution to the problem when the involved 4 × 4 matrices A and B, respectively, have one and three nonzero entries. As a corollary, the problem is solved when A and B have at most four nonzero entries. Our result presents the latest progress on the problem.