Fock-space inseparability criteria of bipartite continuous-variable quantum states

We prove that previous various forms of the inseparability of a Gaussian state are equivalent to the negativity of a partial transposed density matrix in the one-photon Fock subspace. We give an infinite series of inequalities; the fulfillment of each inequality shows the presence of entanglement in bipartite systems. For many non-Gaussian states, we show that Fock-space inseparability criteria are theoretically more efficient and simpler than Shchukin-Vogel criteria, which are based on the moments of the states.