Verifying genuine multipartite entanglement of the whole from its separable parts

Abstract

Ascertaining the large-scale properties of the whole from the properties of its parts is a highly relevant problem in many branches of physics. Here, we investigate a special variant of this task when the parts carry no signs of the global properties in the context of quantum correlation properties in a multipartite optical system. Specifically, we prove experimentally the predicted existence of a three-qubit quantum state with genuine multipartite entanglement (GME) that can be certified solely from its separable two-qubit reduced density matrices. The qubits are encoded into different degrees of freedom of a pair of correlated photons, and the state is prepared by letting the photons propagate through a linear optical circuit. The presence of GME is verified by finding numerically a fully decomposable entanglement witness acting nontrivially only on the reductions of the global state. Our result confirms the viability of detection of emerging global properties of composite quantum systems from the parts that lack the properties.