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arXiv:0808.3690 · Communications in Theoretical Physics

Entanglement Dynamics of Two-Qubit System in Different Types of Noisy Channels

Shan Chuan-Jia, Jibing Liu, Cheng Wei-Wen, Tang-Kun Liu, Huang Yan-Xia, Hong Li

Published Jun 1, 2009• 11 citations
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Abstract

In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.

DOI
10.1088/0253-6102/51/6/10

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In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.
In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states, is investigated. The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.
We investigate the change of entanglement for distributing an arbitrarily entangled two-qubit pure state via three typical kinds of noisy quantum channels—amplitude damping, phase damping and depolarizing quantum channels. We find that for one-qubit transmission, the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the entanglement-decay ratio is determined only by the noisy characteristics of quantum channels. For two-qubit transmission, the rule of the entanglement change is complex. For phase damping quantum channels, the four Bell states and are all the optimal entanglement-distribution (OED) input states. But for amplitude damping quantum channels, only |ψ ± ⟩ are the OED input. For depolarizing quantum channels, and in the case of symmetrical quantum channels, the four Bell states are still the OED input. We also discuss the problem of entanglement sudden death (ESD) and find that for all the three types of quantum channels, ESD can be found.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death (ESD) is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the case with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways.
We investigate the effects of error correction on non-local quantum coherence as a function of time, extending the study by Sainz and Bjork. We consider error correction of amplitude damping, pure phase damping and combinations of amplitude and phase damping as they affect both fidelity and quantum entanglement. Initial two-qubit entanglement is encoded in arbitrary real superpositions of both Φ\PhiΦ-type and Ψ\PsiΨ-type Bell states. Our main focus is on the possibility of delay or prevention of ESD (early stage decoherence, or entanglement sudden death). We obtain the onset times for ESD as a function of the state-superposition mixing angle. Error correction affects entanglement and fidelity differently, and we exhibit initial entangled states for which error correction increases fidelity but decreases entanglement, and vice versa.