Distillability sudden death in qutrit-qutrit systems under amplitude damping

Recently it has been discovered that certain two-qutrit entangled states interacting with global and/or multi-local decoherence undergo distillability sudden death (DSD). We investigate this phenomenon for qutrit-qutrit systems interacting with statistically independent zero-temperature reservoirs. We show that certain initially prepared free-entangled states become bound-entangled in a finite time due to the action of a Markovian dissipative environment. As there is no definitive criterion for separability/entanglement of density matrices with dimension greater than 6, therefore we believe that the results obtained in this paper are restricted to a specific family of states considered here. Moreover, in contrast to local dephasing, simple local unitary transformations can completely avoid distillability sudden death under amplitude damping.