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arXiv:1905.10505 · Journal of Physics A Mathematical and Theoretical

Construction of genuine multipartite entangled states

Yi Shen, Lin Chen

Published Feb 11, 2020• 12 citations

Abstract

Abstract Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to characterize genuine multipartite entangled states, because the genuine multipartite entanglement is unruly. There are scattered results on the criteria for genuine multipartite entangled states. We propose another product based on the Kronecker product in this paper. The Kronecker product is a common product in quantum information with good physical interpretation. We mainly investigate whether the proposed product of two genuine multipartite entangled states is still a genuine entangled one. We understand the entanglement of the proposed product better by characterizing the entanglement of the Kronecker product. Then we show the proposed product is a genuine multipartite entangled state in two cases. The results develop nontrivial criteria for a class of genuine multipartite entangled states. One can use such criteria to systematically construct genuine multipartite entangled states of more parties.

DOI: 10.1088/1751-8121/ab7521

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Abstract Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to characterize genuine multipartite entangled states, because the genuine multipartite entanglement is unruly. There are scattered results on the criteria for genuine multipartite entangled states. We propose another product based on the Kronecker product in this paper. The Kronecker product is a common product in quantum information with good physical interpretation. We mainly investigate whether the proposed product of two genuine multipartite entangled states is still a genuine entangled one. We understand the entanglement of the proposed product better by characterizing the entanglement of the Kronecker product. Then we show the proposed product is a genuine multipartite entangled state in two cases. The results develop nontrivial criteria for a class of genuine multipartite entangled states. One can use such criteria to systematically construct genuine multipartite entangled states of more parties.

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The variety of multipartite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view, classifications have been introduced. Accordingly, here we derive criteria and demonstrate how to experimentally discriminate an observed state against the ones of certain other classes of multipartite entangled states. Our method, originating in Bell inequalities, adds an important tool for the characterization of multiparty entanglement.

We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.

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.

With the development of quantum information processing, multipartite entanglement measures are needed in many cases. However, there are still no complete orthogonal genuine multipartite entanglement (GME) bases available as Bell states to bipartite systems. To achieve this goal, we find a method to construct complete orthogonal GME states, and we exclude many equivalent states by leveraging the group theory. We also provide the case of a 3-order 3-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application. Moreover, we discuss some open questions and believe that this work will enlighten extensive studies in this field.

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.