The three way distributive entanglement is shown to be related to the parallelism of vectors. Using a measurement based approach we form a set of 2-dimensional vectors, representing the post measurement states of one of the parties. These vectors originate at the same point and have an angular distance between them. The area spanned by a pair of such vectors is a measure of the entanglement of formation. This leads to a geometrical manifestation of the 3-tangle in 2-dimensions, from an inequality in area which generalizes for n-qubits to reveal that the n-tangle also has a planar structure. Quantifying the genuine n-party entanglement in every 1|(n − 1) bi-partition, we show that the genuine n-way entanglement does not manifest in n-tangle. A new quantity geometrically similar to 3-tangle is then introduced that represent the genuine n-way entanglement. Extending our formalism to 3-qutrits, we show that the non locality without entanglement arises from a condition under which the post measurement state vectors of a separable state show parallelism. A connection to non trivial sum uncertainty relation analogous to Maccone and Pati uncertainty relation (Maccone and Pati 2014 Phys. Rev. Lett. 113 260401) is then shown using decomposition of post measurement state vectors along parallel and perpendicular direction of the pre-measurement state vectors.
Using the multiparty entanglement of quantum weighted hypergraph states, we built a protocol to build a quantum blockchain. In this protocol, the information contained by the classical blocks is initialized at a single qubit that acts as a vertex of the corresponding hypergraph and the entanglement of the hypergraph state serves the purpose of the "chain." The security and effectiveness of the protocol are then outlined. We further provide a quantum circuit and implement it on IBM's five-qubit computer with single-and two-qubit quantum gates as components.
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