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Register a new userEntanglement monogamy and entanglement evolution in multipartite systems
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We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems. For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here. Moreover, it is found that the initial cavity-cavity entanglement evolves completely to the genuine four-partite cavities-reservoirs entanglement in the time interval between the sudden death of cavity-cavity entanglement and the birth of reservoir-reservoir entanglement. In addition, we also address the relationship between the genuine block-block entanglement form and qubit-block form in the interval.
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We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MoE). We show that all proven MoE relations using concurrence can be rephrased in terms of CREN. Furthermore we show that higher-dimensional (qudit) extensions of MoE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MoE in terms of concurrence. We further test the CREN version of MoE for qudits by considering fully or partially coherent mixtures of a qudit W-class state with the vacuum and show that the CREN version of MoE for qudits is satisfied in this case as well. The CREN version of MoE for qudits is thus a strong conjecture with no obvious counterexamples.
We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the {alpha}th power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
We assess the performance of an entanglement indicator which can be obtained directly from tomograms, avoiding state reconstruction procedures. In earlier work, we have examined this tomographic entanglement indicator, and a variant obtained from it, in the context of continuous variable systems. It has been shown that, in multipartite systems of radiation fields, these indicators fare as well as standard measures of entanglement. In this paper, we assess these indicators in the case of two generic hybrid quantum systems, the double Jaynes-Cummings model and the double Tavis-Cummings model using, for purposes of comparison, the quantum mutual information as a standard reference for both quantum correlations and entanglement. The dynamics of entanglement is investigated in both models over a sufficiently long time interval. We establish that the tomographic indicator provides a good estimate of the extent of entanglement both in the atomic subsystems and in the field subsystems. An indicator obtained from the tomographic indicator as an approximation, however, does not capture the entanglement properties of atomic subsystems, although it is useful for field subsystems. Our results are inferred from numerical calculations based on the two models, simulations of relevant equivalent circuits in both cases, and experiments performed on the IBM computing platform.
We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a set of absolute values of the determinants for each subspace of the multipartite systems. Unlike other schemes, our scheme provides indication of the degrees of entanglement when the qubits are measured or lost successively, and leads naturally to the necessary and sufficient conditions for multipartite pure states to be separable. For systems with a large number of particles, a rougher indication of the degree of entanglement is provided by the set of mean values of the determinantal values for each subspace of the multipartite systems.
We present a simple model together with its physical implementation which allows one to generate multipartite entanglement between several spatial modes of the electromagnetic field. It is based on parametric down-conversion with N pairs of symmetrically-tilted plane waves serving as a pump. The characteristics of this spatial entanglement are investigated in the cases of zero as well as nonzero phase mismatch. Furthermore, the phenomenon of entanglement localization in just two spatial modes is studied in detail and results in an enhancement of the entanglement by a factor square root of N.
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