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arXiv:0912.2868 · Journal of Physics B Atomic Molecular and Optical Physics

Distillability sudden death in qutrit–qutrit systems under amplitude damping

Mazhar Ali

Published Jan 28, 2010• 40 citations
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Abstract

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.

DOI
10.1088/0953-4075/43/4/045504

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Comments on “Distillability sudden death in qutrit—qutrit systems under thermal reservoirs”

Mazhar Ali

In a recent paper ( 2012 Chin. Phys. B 21 084205 ), the authors studied the problem of distillability sudden death. We find that their equation of motion is incorrect and consequently the rest of the paper is wrong. Even apart from starting with a wrong equation of motion, their description of the phenomenon of distillability sudden death is totally misleading and needs to be rectified. To this aim, we show that certain initially prepared free-entangled states become bound-entangled in a finite time under thermal reservoirs. Moreover, in contrast with zero-temperature reservoirs, simple local unitary transformations cannot completely avoid distillability sudden death.

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Distillability sudden death in two-qutrit systems with external magnetic field and Dzyaloshinskii-Moriya interaction due to decoherence

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Recently, Mazhar Ali ( Phys. Rev. A , 81 (2010) 042303 and J. Phys. B , 43 (2010) 045504) showed the phenomenon of distillability sudden death (DSD) in qutrit-qutrit systems under amplitude damping. In this paper, the phenomenon of distillability sudden death in two-qutrit systems which are in the presence of the external magnetic field and Dzyaloshinskii-Moriya (DM) interaction under decoherence has been investigated. With the help of the realignment criterion, we show that certain initial prepared free entangled states may become bound entangled states in a finite time. Moreover, the effects of the external magnetic field strength and the DM interaction parameter, as well as the intrinsic decoherence parameter on the possibility of DSD in our model have been studied in detail.

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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.
Recently Song et al. [Phys. Rev. A 80, 012331 (2009)] discovered that certain two-qutrit entangled states interacting with multilocal dephasing undergo distillability sudden death (DSD). We generalized their studies for quantum states under global, collective, and multilocal dephasing. We found that for a specific family of quantum states DSD and entanglement sudden death may happen under global dephasing as well as under multilocal dephasing. Moreover, for these states simple local unitary transformations may not avoid DSD under the current dynamics. As there is no definitive criterion for separability or entanglement of density matrices with dimensions greater than six, therefore we believe that the results obtained in this article are restricted to the specific family of states considered here.
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.
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.
In a recent paper ( 2012 Chin. Phys. B 21 084205 ), the authors studied the problem of distillability sudden death. We find that their equation of motion is incorrect and consequently the rest of the paper is wrong. Even apart from starting with a wrong equation of motion, their description of the phenomenon of distillability sudden death is totally misleading and needs to be rectified. To this aim, we show that certain initially prepared free-entangled states become bound-entangled in a finite time under thermal reservoirs. Moreover, in contrast with zero-temperature reservoirs, simple local unitary transformations cannot completely avoid distillability sudden death.
Recently, Mazhar Ali ( Phys. Rev. A , 81 (2010) 042303 and J. Phys. B , 43 (2010) 045504) showed the phenomenon of distillability sudden death (DSD) in qutrit-qutrit systems under amplitude damping. In this paper, the phenomenon of distillability sudden death in two-qutrit systems which are in the presence of the external magnetic field and Dzyaloshinskii-Moriya (DM) interaction under decoherence has been investigated. With the help of the realignment criterion, we show that certain initial prepared free entangled states may become bound entangled states in a finite time. Moreover, the effects of the external magnetic field strength and the DM interaction parameter, as well as the intrinsic decoherence parameter on the possibility of DSD in our model have been studied in detail.
Considering the influences of collective dephasing, multilocal qutrit-flip, local qutrit-flip, and the combination of global mixed noise, we study the dynamics of entanglement and the phenomenon of distillability of sudden death (DSD) in a qutrit-qutrit system under various decoherent noises. It is shown that the system always undergoes DSD when it interacts with multilocal and local qutrit-flip noise, and the time-determined bound entangled state is more dependent on different noises. Comparing with the cases of global mixed and collective dephasing noise, we conclude that the qutrit-flip noise is responsible for the DSD.