Superdense Coding and Stabiliser Codes with Ising-coupled Entanglement

A new class of quantum states is introduced by demanding that the computational measurement statistics approach the Boltzmann distribution of higher-order strongly coupled Ising models. The states, referred to as n-coupled states, are superpositions of even or odd parity n-qubit states, generalize Bell states, and form an orthonormal basis for the n-qubit Hilbert space. For any n, the states are maximally connected and locally maximally entangled. It is proven that the n-qubit W and GHZ multipartite entanglement classes have vanishing hyperdeterminant for all n≥ 3 and n≥ 4, respectively, and that the n-coupled states fall in the latter. Still, multiple novel protocols for multi-party secure dense coding and stabiliser code construction are presented, which rely on the structure of n-coupled states as well as symmetry-breaking phase perturbations.