Detecting and embedding high-dimensional genuine multipartite entanglement states

Entanglement of high-dimensional multipartite systems plays an important role both in quantum foundation and applications of quantum physics. Inspired by the genuine high-dimensional entanglement (Kraft et al. in Phys Rev Lett 120:060502, 2018), we first propose a new criterion to characterize genuine entangled states in arbitrary finite dimensional systems. We further define two decomposable models by using embedding method for featuring experimentally untrusted parties. We show that the equivalence of local decomposability and embedded decomposability holds under special conditions for entangled pure states. For mixed states, we show the decomposability may be changed in embedded space.

Automated summary

Entanglement of high-dimensional multipartite systems is crucial in both fundamental quantum theory and practical applications. This study proposes a new criterion to characterize genuine entangled states in arbitrary finite dimensional systems, inspired by the genuine high-dimensional entanglement. Two decomposable models are defined using the embedding method to address the issue of untrusted parties in experiments. The study shows the equivalence of local decomposability and embedded decomposability under specific conditions for entangled pure states, while for mixed states, the decomposability may change in the embedded space.