Distillability sudden death in qutrit-qutrit systems under global and multilocal dephasing

Abstract

Recently Song et al., Phys. Rev. A 80, 012331 (2009), have discovered that certain two-qutrit entangled states interacting with multi-local decoherence undergo distillability sudden death whereas their locally equivalent states do not exhibit such behavior. We have found that their basic equation of motion missed some terms and therefore the subsequent calculations and conclusions are not correct/valid except that distillability sudden death may occur. We provide the missing terms and point out the corrections which must be done in the literature to remove confusion. Moreover, we have studied this feature for certain entangled states under global, collective and multi-local decoherence. We have found that entanglement sudden death and distillability sudden death may happen under global and multi-local noises. Moreover, local unitary transformations can not avoid distillability sudden death.

Distillability sudden death and sudden birth in a two-qutrit system under decoherence at finite temperature

“…However, it is worth noting that this realignment criterion cannot detect the whole entanglement at time t > 0.093. This result agrees with previous studies for qutrit-qutrit systems in dissipative environments [21,[23][24][25][26][27][28].…”

“…Some people have already studied these states for almost all local Markovian channels available [21][22][23][24][25][26]. In Eq.…”

“…Based on Refs. [21][22][23][24][25][26][27][28][29][30], for a separable state ρ, the negativity is zero or negative, namely N (ρ) ≤ 0, and the realignment criterion implies that R(ρ) ≤ 0. For a positive partial transpose (PPT) state, the realignment criterion R(ρ) > 0 can prove the bound entangled state.…”

“…On the contrary, when an initially prepared in bound entangled or separable state becomes a distillable entangled state in a finite time, then it is said that it undergoes distillability sudden birth [22]. Recently great attention has been paid to the development of works on distillability sudden death [23][24][25][26][27][28][29][30] and sudden birth [31][32][33] addressing the practical problems of environmental decoherence. For example, Mazhar Ali investigated distillability sudden death of two-qutrit systems in the presence of either collective or multilocal noises [23,24].…”

“…Recently great attention has been paid to the development of works on distillability sudden death [23][24][25][26][27][28][29][30] and sudden birth [31][32][33] addressing the practical problems of environmental decoherence. For example, Mazhar Ali investigated distillability sudden death of two-qutrit systems in the presence of either collective or multilocal noises [23,24]. This behavior of distillability sudden death was later extended to two-qutrit systems interacting with thermal reservoirs [25,26] as well as in the presence of the external magnetic field [27,28].…”