Origin of noisy states whose teleportation fidelity can be enhanced through dissipation

Recently, Badziag et al. [Phys. Rev. A 62, 012311 (2000)] obtained a class of noisy states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via an amplitude damping channel (ADC). We show that such noisy states result while sharing the states $|{\ensuremath{\Phi}}^{\ifmmode\pm\else\textpm\fi{}}〉=1/\sqrt{2}(|00〉\ifmmode\pm\else\textpm\fi{}|11〉)$ across the ADC. We also show that under similar dissipative interactions, different Bell states give rise to noisy entangled states that are qualitatively very different from each other in the sense that only the noisy entangled states constructed from the Bell states $|{\ensuremath{\Phi}}^{\ifmmode\pm\else\textpm\fi{}}〉$ can sometimes be made better by subjecting the unaffected qubit to a dissipative interaction with the environment. Importantly, if the noisy state is nonteleporting, then it can always be made teleporting with this prescription. We derive the most general restrictions on improvement of such noisy states assuming that the damping parameters are different for both qubits. However, this curious prescription does not work for the noisy entangled states generated from $|{\ensuremath{\Psi}}^{\ifmmode\pm\else\textpm\fi{}}〉=1/\sqrt{2}(|01〉\ifmmode\pm\else\textpm\fi{}|10〉).$ This shows that an a priori knowledge of the noisy channel might be helpful in order to decide which Bell state needs to be shared between Alice and Bob.