  In a previous paper tests for entanglement for two mode systems involving
identical massive bosons were obtained. In the present paper we consider
sufficiency tests for EPR steering in such systems. We find that spin squeezing
in any spin component, a Bloch vector test, the Hillery-Zubairy planar spin
variance test and squeezing in two mode quadratures all show that the quantum
state is EPR steerable. We also find a generalisation of the Hillery-Zubairy
planar spin variance test for EPR steering. The relation to previous
correlation tests is discussed. This paper is based on a detailed
classification of quantum states for bipartite systems. States for bipartite
composite systems are categorised in quantum theory as either separable or
entangled, but the states can also be divided differently into Bell local or
Bell non-local states in terms of local hidden variable theory (LHVT). For the
Bell local states there are three cases depending on whether both, one of or
neither of the LHVT probabilities for each sub-system are also given by a
quantum probability involving sub-system density operators. Cases where one or
both 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 local
states where there is no LHS, or the Bell non-local states. The relationship
between the quantum and hidden variable theory classification of states is
discussed.
