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arXiv:1106.4257 · Physical Review A

Quantum entanglement in multiparticle systems of two-level atoms

Ram Narayan Deb

Published Sep 19, 2011• 6 citations
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Abstract

We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express the inherent quantum fluctuations of a composite system of two-level atoms as a sum of the quantum fluctuations of the individual constituent atoms and their correlation terms. This helps to separate out and study solely the quantum correlations among the atoms and obtain the criterion for the presence of entanglement in such multiatomic systems.

DOI
10.1103/physreva.84.032327

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We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express the inherent quantum fluctuations of a composite system of two-level atoms as a sum of the quantum fluctuations of the individual constituent atoms and their correlation terms. This helps to separate out and study solely the quantum correlations among the atoms and obtain the criterion for the presence of entanglement in such multiatomic systems.
We propose a direct measure of tripartite quantum entanglement in an arbitrary symmetric pure state of N correlated two-level atoms (qubits). We compute the third order moments of the collective pseudo-spin operators in terms of the individual atomic operators of the atoms in the assembly and find that all the bipartite quantum correlation terms among the atoms cancel out leaving only the all possible tripartite quantum correlation terms among them. We observe that the third order moments are made up of solely the tripartite quantum correlations among the atoms. This helps to extract out only the tripartite quantum correlations among the N atoms and propose a measure and quantification of these correlations. We also propose the necessary and sufficient condition for the presence of tripartite quantum entanglement in such multi-atomic systems. We conjecture the way of determining the third order moments of the pseudo-spin operators of the two-level atoms in the assembly, experimentally.
The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that a state is separable iff $| \mathbf{C}(ρ)| $ =0 for pure states and iff C(ρ)C(ρ)C(ρ) vanishes for mixed states.
The problem of the impossibility of completely describing the quantum entanglement of a system of many particles only with the biparticle entanglement of the constituent subsystems is treated. The numerical procedure of the selection of a contrary instance and the results of the procedure are described. It is also shown that the measure of the entanglement of pure states on the basis of the minimization of the entropy of measurements is essentially a multiparticle measure; i.e., this measure of entanglement cannot be expressed in terms of the Schmidt coefficients.
Entanglement is deemed a valuable resource for quantum computing and lies at the heart of quantum information. At the same time, current experiments are venturing into the realm of quantum systems consisting of many particles. In this book, different aspects of entanglement and non-locality in multiparticle systems are investigated. First, it presents an approach for an experimental verification of non-locality and entanglement with a high statistical significance. Second, a criterion for genuine multiparticle entanglement is introduced. Furthermore, this criterion also allows for a way of quantifying multiparticle entanglement. Analytical criteria for entanglement in a special class of quantum states, so-called graph states, are presented. These criteria turn out to be also necessary for entanglement in certain cases. Finally, ways of generalizing a non-local hidden-variable model proposed by Leggett are shown.
In this work, decoherence of a system from an entangled state is studied theoretically by computing the time-dependent probability amplitude with which the system remains in that state. The system is composed of, in addition to vacuum, identical two-level atoms that interact indirectly with each other through photons and have a uniform distribution in the vacuum. Under the assumption that in the initial entangled state only one atom is allowed to be in the excited state, a general expression for the probability amplitude is obtained and applied to two specific entangled states, one symmetric and one antisymmetric, to demonstrate that the system decoheres from these two states at the same rate under certain conditions.