Variational estimation of entanglement entropy for bipartite many-body systems

Abstract

We explore a variational characterization of the bipartite entanglement entropy such as von Neumann entropy for pure states in terms of general projective measurements of an arbitrary system. By properly choosing the measurement basis, we show that a general estimation of the bipartite entanglement measure can be explicitly written. The number of projective measurement operators of the subsystem necessary for calculating an upper bound of the bipartite entanglement entropy is less than or equal to the dimension of the smaller subsystem. This number is much smaller than that of the full tomography of the density matrix. As an application, our method is useful to estimate the entanglement entropy of each energy eigenstate of a given Hamiltonian.