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In a previous paper tests for entanglement for two mode systems involvingidentical massive bosons were obtained. In the present paper we considersufficiency tests for EPR steering in such systems. We find that spin squeezingin any spin component, a Bloch vector test, the Hillery-Zubairy planar spinvariance test and squeezing in two mode quadratures all show that the quantumstate is EPR steerable. We also find a generalisation of the Hillery-Zubairyplanar spin variance test for EPR steering. The relation to previouscorrelation tests is discussed. This paper is based on a detailedclassification of quantum states for bipartite systems. States for bipartitecomposite systems are categorised in quantum theory as either separable orentangled, but the states can also be divided differently into Bell local orBell non-local states in terms of local hidden variable theory (LHVT). For theBell local states there are three cases depending on whether both, one of orneither of the LHVT probabilities for each sub-system are also given by aquantum probability involving sub-system density operators. Cases where one orboth are given by a quantum probability are known as local hidden states (LHS)and such states are non-steerable. The steerable states are the Bell localstates where there is no LHS, or the Bell non-local states. The relationshipbetween the quantum and hidden variable theory classification of states isdiscussed.

Quantum Theory and Local Hidden Variable Theory: General Features and Tests for EPR Steering