Evolution reconstruction of deviate Bell states by extending the novel Fourier-based method
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Evolution reconstruction of deviate Bell states by extending the novel Fourier-based method Hua Zhou1 · Guangxia Li1 · Wenming Zhu1 · Yang Su1 · Tao Pu1 · Zhiyong Xu1 · Jingyuan Wang1 · Yimin Wang1 · Jianhua Li1 · Huiping Shen1 Received: 24 February 2020 / Accepted: 3 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The time-variant quantum communication channel affected by uncontrollable environmental factors induces an unrepeatable evolution of Bell states, which calls for a universal method of evolution reconstruction. The novel Fourier-based method proposed recently is extended and demonstrated for the deviated Bell states. The density operators are represented in terms of expectation value functions of projectors. The optimal quorums and measurement schemes are presented. The ways of extending the Fourier-based recovery series are also given. The simulated results show that our method is effective and the novel Fourier-based method can keep a good performance for the evolution reconstruction of Bell states. Keywords Evolution reconstruction · Bell states · Novel Fourier-based method · Projective measurement
1 Introduction Quantum state tomography (QST) is a very useful tool to validate and exploit quantum resources by performing a series of measurements and reconstructing quantum states from measurement results [1–6]. Common QST concerns the state on a specific moment, but time evolution reconstruction goes further to show all of the state information in a time period by revealing kinds of correlations in the time domain [7–13]. Entangled states are widely used resources in quantum information, of which Bell states are the most fundamental ones utilized in quantum communication [14–17]. QST for Bell states has been used to determine the output state and its fidelity [18].
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Hua Zhou [email protected] College of Communication Engineering, Army Engineering University of PLA, Nanjing 210007, China 0123456789().: V,-vol
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But the channel, either the optical fiber or the atmosphere, is always time variant [19, 20]. The evolution of quantum states induced by uncontrollable environmental factors along the communication channel cannot be repeated, which is much different from normal evolution reconstruction context [21]. Therefore, a universal method of evolution reconstruction is needed for deviate Bell states. Recently, a novel Fourier-based method of reconstructing any evolution with bandlimited expectation value functions of projectors has been proposed [22]. This method makes use of projectors and is independent of the system Hamiltonian, which fits quantum communication perfectly. But it has only been demonstrated on a two-dimensional state. In this paper, we extend this novel Fourier-based method onto Bell states. We first represent deviate Bell states in terms of expectation value functions of projectors which are the products of sub-projectors for reconstructing a two-dimensional state. Then, we introduce the optimal quorums and p
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