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arXiv:2003.07153

New Genuine Multipartite Entanglement

Luo, Ming-Xing

Published Mar 16, 2020• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2003.07153

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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 333. 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.
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Quantum networks are under current active investigation for the implementation of quantum communication tasks. With this motivation in mind, we study the entanglement properties of the multipartite states underlying these networks. We show that, in sharp contrast to the case of pure states, genuine multipartite entanglement is severely affected by the presence of noise depending on the network topology: the amount of connectivity determines whether genuine multipartite entanglement is robust for any system size or whether it is completely washed out under the slightest form of noise for a sufficiently large number of parties. The impossibility to obtain genuine multipartite entanglement in some networks implies some fundamental limitations for their applications. In addition, the family of states considered in this work proves very useful to find new examples of states with interesting properties. We show this by constructing states of any number of parties that display superactivation of genuine multipartite nonlocality.
Sharing genuine multipartite entanglement by considering collective use of copies of biseparable states, which are entangled across all bipartitions but lack genuine multipartite entanglement at the single-copy level, plays a central role in several quantum information processing protocols, and has been referred as genuine multipartite entanglement activation. We present a protocol for three-qutrit systems showing that two copies of rank-two biseparable states, entangled across every bipartition, are sufficient to generate a genuinely multipartite entangled state with nonzero probability. This contrasts with the three-qubit scenario where many copies of biseparable states might be required for sharing genuine multipartite entanglement. We subsequently generalize our protocols to the case of an arbitrary number of parties. Interestingly, the proposed construction naturally leads to the activation of genuinely nonlocal correlations, yielding a result that is stronger than genuine multipartite entanglement activation alone.
Genuine multipartite entanglement (GME) is considered a powerful form of entanglement since it corresponds to those states that are not biseparable, i.e. a mixture of partially separable states across different bipartitions of the parties. In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e. several copies of a biseparable state can display GME. We show that the set of GME-activatable states admits a simple characterization: a state is GME-activatable if and only if it is not partially separable across one bipartition of the parties. This leads to the second question of whether there is a general upper bound in the number of copies that needs to be considered in order to observe the activation of GME, which we answer in the negative. In particular, by providing an explicit construction, we prove that for any number of parties and any number k∈N there exist GME-activatable multipartite states of fixed (i.e. independent of k ) local dimensions such that k copies of them remain biseparable.
Abstract Quantum entanglement and quantum entropy are crucial concepts in the study of multipartite quantum systems. In this work, we show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and computational tools for the analysis of both. In particular, using this approach for a general multipartite pure state, one can easily prove known relations in an easy way and to build up new relations between the concurrences associated with the different bipartitions. The approach is also useful to derive sufficient conditions for genuine entanglement in generic multipartite systems that are computable in polynomial time. From an entropy-of-entanglement perspective, the approach is powerful to prove properties of the Tsallis-2 entropy, such as the subadditivity, and to derive new ones, e.g., a modified version of the strong subadditivity which is always fulfilled; thanks to the purification theorem these results hold for any multipartite state, whether pure or mixed.