Hyperdeterminant of 4-qubit spin chains

Abstract

The properties of the hyperdeterminant, a genuine multipartite entanglement figure of merit for 4 qubits, are studied. We analyze when the hyperdeterminant detects quantum phase transitions and how it is related to the wave function of the system. By studying the ground state of two well-known quantum hamiltonians, Ising and XXZ, we analyze how entanglement behaves in terms of the hyperdeterminant. To conclude, we introduce finite temperature effects which leads us to explore the full spectrum of energies of both models.