  A new additive and semidefinite programming (SDP) computable entanglement
measure is introduced to upper bound the amount of distillable entanglement in
bipartite quantum states by operations completely preserving the positivity of
partial transpose (PPT). This quantity is always smaller than or equal to the
logarithmic negativity, the previously best known SDP bound on distillable
entanglement, and the inequality is strict in general. Furthermore, a succinct
SDP characterization of the one-copy PPT deterministic distillable entanglement
for any given state is also obtained, which provides a simple but useful lower
bound on the PPT distillable entanglement. Remarkably, there is a genuinely
mixed state of which both bounds coincide with the distillable entanglement
while being strictly less than the logarithmic negativity.
