Quantum Theory and Local Hidden Variable Theory: General Features and Tests for EPR Steering. (arXiv:1611.09101v4 [quant-ph] UPDATED)

Quantum states for bipartite composite systems are categorised as either
separable or entangled, but the states can also be divided differently into
Bell local or Bell non-local states. This paper presents a detailed
classification of quantum states for bipartite systems and describes the
interrelationships between the various types. For the Bell local states there
are three cases depending on whether both, one of or neither of the local
hidden variable theory 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. 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 the any spin
component, a Bloch vector test, the Hillery-Zubairy planar spin variance test
and a two mode quadrature squeezing test all show that the LHS model fails, and
hence 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.

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