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Chinese Physics Letters

Distillability of Sudden Death in Qutrit-Qutrit Systems under Global Mixed Noise*

Bing-Bing Chai, Jin‐Liang Guo

Published May 1, 2019• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0256-307x/36/5/050303

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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.
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.
Entanglement dynamics of a qutrit-qutrit system under the influence of global, local and multilocal decoherence introduced by phase flip, trit flip and trit phase flip channels is investigated. The negativity and realignment criterion are used to quantify the entanglement of the system. It is shown that the entanglement sudden death and distibility sudden death can be avoided in the presence of phase flip, trit flip and trit-phase flip environments. It is shown that certain free entangled distillable qutrit states become bound entangled or separable i.e. convert into non-distillable states under different flipping noises. It is also seen that local operations do not have any effect on the entanglement dynamics of the system. Further more, no ESD and DSD is seen for the case of trit flip channel.
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.
In this paper we study the dynamics of entanglement in some hybrid qubit–qutrit systems under the influence of global, collective, local and multilocal depolarising noise. We show that depolarising noise can be used to induce entanglement. A critical point exists under every coupling of the system with the environment at which all the states are equally entangled. Furthermore, we show that no ESD occurs when either only the qubit is coupled to its local environment or the system is coupled to a multilocal or global environment. This is an important result for various quantum information processing tasks and thus merits further investigation.
We introduce the concept of distillability sudden death, i.e., free entangled states can evolve into nondistillable (bound entangled or separable) states in finite time under local noise. We describe the phenomenon through a specific model of local dephasing noise and compare the behavior of states in terms of the Bures fidelity. Then we propose a few methods to avoid distillability sudden death of states under (general) local dephasing noise so that free entangled states can be robust against decoherence. Moreover, we find that bound entangled states are unstable in the limit of infinite time.
The effect of decoherence on a qubit-qutrit system under the influence of global and multilocal decoherence in non-inertial frames is investigated. It is shown that the entanglement sudden death (ESD) can be avoided in non-inertial frames in the presence of dephasing and bit-trit phase flip channels for entire range of decoherence. However, ESD behaviour is seen for higher level of decoherence in case of phase flip and bit-trit flip channels. Irrespective of the entanglement degradation caused by the Unruh effect, no ESD occurs for the dephasing environment. Furthermore, flipping channels have approximately similar effect on the entanglement of the hybrid system.