Distillability sudden death in a two qutrit systems under a thermal reservoir

Abstract

The dynamics of distillability entanglement between qutrit—qutrit systems interacting with a thermal reservoir is investigated in this paper. We discovered an interesting phenomenon that under a thermal reservoir certain initially prepared free-entangled states become bound-entangled states in a finite time, which is called distillability sudden death (DSD). We use a realignment criterion to measure the nine-dimensional density matrix of the entanglement. Moreover, we analyze some other parameters to investigate the effects to the systems. Explanations are then given.

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

“…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].…”

“…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]. Derkacz and Jakóbczyk demonstrated the revivals of distillable entanglement for two identical three-level atoms coupled to the common vacuum [31][32][33].…”

“…To the contrary, if an initial prepared in bound entangled or separable states becomes distillable entangled states, then it is said that it undergoes distillability sudden birth [15]. Recently great attention has been paid to the development of work on distillability sudden death [16][17][18][19][20][21][22][23] and sudden birth [24][25][26] addressing the practical problems of environmental decoherence. In particular, under certain types of environment interaction, certain distillable entangled states may be converted into bound entangled or separable states in a finite time and vice versa.…”