We exhibit a two-parameter family of bipartite mixed states rho(bc), in a d
xd Hilbert space, which are negative under partial transposition (NPT), but
for which we conjecture that no maximally entangled pure states in 2x2 can
be distilled by local quantum operations and classical communication (LQ+C
C). Evidence for this undistillability is provided by the result that, for
certain states in this family, we cannot extract entanglement from any arbi
trarily large number of copies of rho(bc) using a projection on 2x2. These
states are canonical NPT states in the sense that any bipartite mixed state
in any dimension with NPT can be reduced by LQ+CC operations to a NPT stat
e of the rho(bc) form. We show that the main question about the distillabil
ity of mixed states can be formulated as an open mathematical question abou
t the properties of composed positive linear maps.