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Register a new userMaximum $N$-body correlations do not in general imply genuine multipartite entanglement
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The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong $N$-party correlations with $N$-party entanglement in an $N$-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest $N$-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest $N$-party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation.
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Beyond the simplest case of bipartite qubits, the composite Hilbert space of multipartite systems is largely unexplored. In order to explore such systems, it is important to derive analytic expressions for parameters which characterize the systems state space. Two such parameters are the degree of genuine multipartite entanglement and the degree of mixedness of the systems state. We explore these two parameters for an N-qubit system whose density matrix has an X form. We derive the class of states that has the maximum amount of genuine multipartite entanglement for a given amount of mixedness. We compare our results with the existing results for the N=2 case. The critical amount of mixedness above which no N-qubit X-state possesses genuine multipartite entanglement is derived. It is found that as N increases, states with higher mixedness can still be entangled.
The existence of non-local quantum correlations is certainly the most important specific property of the quantum world. However, it is a challenging task to distinguish correlations of classical origin from genuine quantum correlations, especially when the system involves more than two parties, for which different partitions must be simultaneously considered. In the case of mixed states, intermediate levels of correlations must be introduced, coined by the name inseparability. In this work, we revisit in more detail such a concept in the context of continuous-variable quantum optics. We consider a six-partite quantum state that we have effectively generated by the parametric downconversion of a femtosecond frequency comb, the full 12 x 12 covariance matrix of which has been experimentally determined. We show that, though this state does not exhibit genuine entanglement, it is undoubtedly multipartite-entangled. The consideration of not only the entanglement of individual mode-decompositions but also of combinations of those solves the puzzle and exemplifies the importance of studying different categories of multipartite entanglement.
The standard definition of genuine multipartite entanglement stems from the need to assess the quantum control over an ever-growing number of quantum systems. We argue that this notion is easy to hack: in fact, a source capable of distributing bipartite entanglement can, by itself, generate genuine $k$-partite entangled states for any $k$. We propose an alternative definition for genuine multipartite entanglement, whereby a quantum state is genuinely network $k$-entangled if it cannot be produced by applying local trace-preserving maps over several $k$-partite states distributed among the parties, even with the aid of global shared randomness. We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of entangled systems compared with quantum multisource networks. We prove that any symmetric entangled pure state shows stronger nonlocality than the genuinely multipartite nonlocality in the biseparable model. Similar results hold for other entangled pure states with local dimensions no larger than $3$. We further provide computational conditions for witnessing the new nonlocality of noisy states. These results suggest that the present model is useful characterizing a new kind of generic quantum entanglement.
Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, we give an approach of constituting genuine $m$-partite entanglement measure from any bipartite entanglement and any $k$-partite entanglement measure, $3leq k<m$.In addition, as a complement to the three-qubit concurrence triangle proposed in [Phys. Rev. Lett., 127, 040403], we show that the triangle relation is also valid for any other entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.
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