Lower bound of entanglement of formation based on correlation matrix

The entanglement of formation (EOF), which quantifies the required minimally physical resources to prepare a quantum state, plays important roles in many quantum information processes. Due to the convex-roof definition, it is hard to find the explicit analytic formulae of EOF, except for some special quantum systems. The correlation matrix of a quantum state is closely related to entanglement property. In this paper, we use the Lagrange-multiplier approach to obtain an analytic lower bound of EOF for arbitrary dimensional bipartite states, which improves the previous conclusions. Numerical example shows that the bound is also valid for some PPT entangled states. •We use the Lagrange-multipliers approach to obtain an analytic lower bound of entanglement of formation for arbitrary dimensional bipartite states.•The lower bound is constructed with the trace norm of the correlation matrix of a quantum state.•The lower bound can detect some PPT entangled states.