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Chinese Physics Letters

Entanglement Dynamics of Arbitrary Two-Qubit Pure States under Amplitude and Phase Damping Channels

Feng-Jian Jiang, Ming-Jun Shi, Jiangfeng Du

Published Feb 1, 2011• 3 citations
Publisher

Abstract

Analytic results are presented for the entanglement evolution for arbitrary two-qubit pure state under amplitude damping and particularly phase damping channel. The disentanglement time and the relationship between it and the form of initial state are given explicitly. The lower bounds of disentanglement time are obtained and shown to be the monotone functions of initial concurrence.

DOI
10.1088/0256-307x/28/2/020308

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Analytic results are presented for the entanglement evolution for arbitrary two-qubit pure state under amplitude damping and particularly phase damping channel. The disentanglement time and the relationship between it and the form of initial state are given explicitly. The lower bounds of disentanglement time are obtained and shown to be the monotone functions of initial concurrence.
This paper investigates the change of entanglement for transmitting an arbitrarily entangled two-qubit pure state via one of three typical kinds of noisy quantum channels: amplitude damping quantum channel, phase damping quantum channel and depolarizing quantum channel. It finds, in all these three cases, that the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the decaying ratio is determined only by the noisy characteristics of quantum channels and independent of the form of initial input state.
We discuss entanglement evolution of a multiqubit system in which one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multiqubit concurrence is derived. Using this evolution equation, the entanglement dynamics of an initially mixed three-qubit state composed of a Greenberger-Horne-Zeilinger (GHZ) and a WWW state is analyzed if one of the qubits is affected by a phase, an amplitude, or a generalized amplitude damping channel.
Quantum correlations between two or more different degrees of freedom of the same particle are sometimes referred to as intraparticle entanglement. In this work, we study these intraparticle correlations between two different degrees of freedom under various decoherence channels, viz. amplitude damping, depolarizing, and phase damping channels. We mainly focus on the amplitude-damping channel for which we obtain an exact analytical expression for the concurrence of an arbitrary initial pure state. In this channel, we observe the unique feature of entanglement arising from a separable initial state. We show that this channel allows for a revival of entanglement with an increasing damping parameter, including from a zero value of the concurrence. We also consider the amplitude-damping channel for interparticle entanglement and show that it does not display any of the above-mentioned interesting features. Further, for comparable parameters, the decay of entanglement in the interparticle system is much greater than in the intraparticle system, which we also find to be true for the phase damping and depolarizing channels. Thus, intraparticle entanglement subjected to damping is much more robust than interparticle entanglement.
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.
We propose a scheme to enhance entanglement from amplitude damping or correlated amplitude damping decoherence. We show that entanglement sudden death time can be prolonged by the initial single-qubit operation combined with local filtering operation. For the amplitude damping channel case, we give the optimal single-qubit operation for arbitrary pure state [Formula: see text]. For the correlated amplitude damping channel case, we find that single-qubit operation on the initial state can not only enhance the final entanglement but also avoid entanglement sudden death. Compared to the previous schemes, the optimal operations and local filtering operations used in our scheme are independent with the decay parameters of the environment.
We present a detailed analysis on disentanglement dynamics of multiqubit GHZ-type states whose qubits are remotely located in absence of any mutual interactions. The dynamics is thus induced by independent local environments surrounding each qubit. It has recently been known that if each qubit is subjected solely to the phase damping then the state's entanglement vanishes asymptotically in time and if only the amplitude damping is active then the state's entanglement may vanish suddenly in certain parameter subspace. In this paper, we shall show that a combined action of both the phase damping and the amplitude damping will force the state's entanglement to always vanish suddenly in the entire parameter space. Furthermore, we shall prove that by proper local operations such a finite-time disentanglement can be avoided for whatever state's parameters, no matter the phase damping and the amplitude damping act severally or in combination.