Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

Abstract

Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing phenomenon of quantum mechanics, is a useful quantum resource for quantum communication. Understanding the type of EPR steering in a graph state is the basis for application of it in a quantum network. In this paper, we present EPR steering in a Gaussian weighted graph state, including a linear tripartite and a four-mode square weighted graph state. The dependence of EPR steering on weight factor in the weighted graph state is analyzed. Gaussian EPR steering between two modes of a weighted graph state is presented, which does not exist in the Gaussian cluster state (where the weight factor is unit). For the four-mode square Gaussian weighted graph state, EPR steering between one and its two nearest modes is also presented, which is absent in the four-mode square Gaussian cluster state. We also show that Gaussian EPR steering in a weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy relation. The presented results are useful for exploiting EPR steering in a Gaussian weighted graph state as a valuable resource in multiparty quantum communication tasks.I.

Enhancement of multimode entanglement and asymmetric steering by noiseless linear amplification

“…This is due to the restriction of the monogamy relation as shown in [45]: one mode cannot be steered by two distinct modes simultaneously. According to [46][47][48], the GHZ state is fully symmetric under mode permutations. Thus, if Â′ could be steered by B, it should be equally steered by Ĉ too, which is forbidden by the monogamy relation.…”

Quantum network based on non-classical light

“…In the same year, Qin et al [108] realized the manipulation of the direction of Gaussian EPR steering in noisy environment. Wang et al also proposed the swapping schemes for Gaussian EPR steering between two space-separated entangled states [109,110], and presented EPR steering in a Gaussian weighted graph state [111], which can be used to construct a quantum network of quantum steering.…”

Three-color and tripartite steering generated by intracavity cascaded processes

“…The one-way steering has been proved in theory 10,11 and has been observed in experiments. 5,12,13 Recently, the monogamy relations for EPR steering have been analyzed theoretically in the multipartite state [14][15][16] and demonstrated experimentally. 17 In practical application, steering plays an important role in quantum secret sharing 14 and one-sided device independent quantum communication.…”

“…18 Due to the need of constructing large-scale quantum networks, the research of steering has been extended to multipartite steering systems. At present, there are two schemes to generate multipartite steering: one scheme is implemented by squeezed state and beam splitter; 15,[21][22][23][24][25] however, only optical modes of single frequency can be obtained using the beam splitter network. The other scheme is achieved by cascaded nonlinear processes; this scheme can obtain multicolor continuous variable optical modes, which can be applied to quantum storage, transmission, and processing of broadband at different frequencies in quantum communication networks.…”