Invited PaperDynamics and improvement of quantum correlations in the triple Jaynes–Cummings model
Introduction
Quantum entanglement [1], [2], [3], [4] is not only a distinctive quantum feature of quantum theory which distinguishes between the quantum and classical worlds, but also an essential resource for quantum information processing (QIP) such as quantum communication and quantum computation [5]. Besides quantum entanglement, some other quantum correlations are crucial components of quantum-information theory, which display the quantum advantage without any entanglement [6], [7], [8]. Among the quantum-correlation measures, quantum discord [9], defined as the discrepancy between quantum mutual information and the classical aspect of correlation, has received much attention in studies recently [10], [11], [12]. Thus, quantum entanglement and quantum discord as well as some other measures are useful measurements in describing quantum correlations for the bipartite systems. However, as the dimensions of the subsystems increasing, the computation of multipartite quantum correlations becomes formidably complicated. A few exact formulae for multipartite quantum correlations have been given only in some special cases [13], [14], [15]. Therefore, how to quantify and understand the multipartite quantum correlations is still the subject of active research.
On the other hand, it is shown that decoherence, often caused by the unavoidable interaction of any real quantum systems with their surrounding environments, leads to degradation of entanglement with time and, in certain circumstances, entanglement sudden death (ESD) [16], [17]. Thus it is of great importance to improve entanglement for a sufficiently long time for many interested applications. To achieve this objective, many theoretical efforts have been paid to investigate this subject [18], [19], [20]. In particular, Kim et al. [20] showed that weak measurement and quantum measurement reversal can effectively suppress amplitude-damping decoherence, and even can avoid the ESD. Now the approach of weak measurement and quantum measurement reversal is also extensively applied to the entanglement dynamics of two qubits interacting with various environments [21], [22], [23], [24]. However, the studies of the improvement of multipartite entanglement using the similar approach are scarce [25], [26]. Motivated by the above-mentioned idea, in this work, we will study the dynamics and improvement of tripartite entanglement in a triple Jaynes–Cummings model. Meanwhile, considering genuinely multipartite concurrence [27], the study can be directly generalized to N qubits. By investigation, we find that the entanglement transfer can be significantly controlled through the different initial states. Comparing with tripartite entanglement, the dynamics of the geometric measure of quantum discord [28], [29] is more robust. Furthermore, by applying weak measurement and quantum measurement reversal, we present a scheme to improve tripartite entanglement under certain conditions.
After this introduction, in Section 2 we recall some measurements for multipartite quantum correlations, such as genuinely multipartite concurrence, lower bound of concurrence and geometric measure of quantum discord. In Section 3, we introduce the model for our system and study the relationship between entanglement transfer and the initial state, and the robustness of quantum correlations. In Section 4, we analyze the improvement of tripartite entanglement by performing weak measurement and quantum measurement reversal. Finally, we conclude in Section 5.
Section snippets
Measures of multipartite quantum correlations
In this paper we will briefly review the definitions as well as the general formalism for several measures of quantum correlations, and those measures will be used to quantify and analyze our results. To begin with, we adopt genuinely multipartite concurrence to study multipartite entanglement [14], [25], [27], [30]. For the special case of the N-qubit states whose nonzero elements are only along the diagonal and anti-diagonal, the general expression of X-form matrix can be written as
Correlation dynamics
We consider the triple Jaynes–Cummings model in which three initially correlated two-level atoms A, B and C are independently coupled to three spatially separate single-mode cavities a, b and c, respectively. The subsystems Aa, Bb and Cc have no direct interactions, thus the Hamiltonian of the total system can be obtained by three individual atom-cavity subsystems, which can be written as ()where ω and ω0 represent the transition frequency of
Improving of tripartite entanglement
In what follows, we consider how entanglement of three atoms for the initial GHZ state and W state is enhanced and how ESD is avoided by using the weak measurement and quantum measurement reversal. Firstly, before the atoms couple to the cavities, they are individually subject to weak measurements with the same strengths p, which only partially collapses the state towards . The weak measurement can be denoted as a non-unitary quantum operation , where . Then each atom
Conclusion
In conclusion, we have investigated the dynamics of three atoms and C locally coupled with three independent cavities and c, via the concepts of genuinely multipartite concurrence, lower bound of concurrence and tripartite geometric quantum discord. We choose the GHZ state and the W state as atomic initial states, but the same vacuum state as the initial state of their cavities. It is shown that in the case of the initial GHZ state, the ESD for atoms and the ESB for cavities occur at
Acknowledgments
This work is supported by National Natural Science Foundation of China under Grant nos. 61178012, 11204156, and 11304179, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant nos. 20133705110001 and 20123705120002, the Provincial Natural Science Foundation of Shandong under Grant nos. BS2013DX034 and ZR2014AP009.
References (34)
- et al.
Opt. Commun.
(2011) - et al.
Physica A
(2015) Phys. Rev. Lett.
(1998)- et al.
Phys. Rev. A
(2007) - et al.
Phys. Rev. A
(1996) - et al.
Quantum Computation and Quantum Information
(2000) - et al.
Phys. Rev. Lett.
(1998) - et al.
Phys. Rev. A
(2005) - et al.
Phys. Rev. A
(2006) - et al.
Phys. Rev. Lett.
(2001)
Phys. Rev. A
Phys. Rev. A
Eur. Phys. J. D
Eur. Phys. J. D
Phys. Rev. A
Phys. Rev. Lett.
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