  We examine the prospect of demonstrating Einstein-Podolsky-Rosen (EPR)
entanglement for massive particles using spin-changing collisions in a spinor
Bose-Einstein condensate. Such a demonstration has recently been attempted by
Gross et al. [Nature 480, 219 (2011)] using a condensate of Rb-87 atoms trapped
in an optical lattice potential. For the condensate initially prepared in the
(F,m_{F})=(2,0) hyperfine state, with no population in the m_{F}=+-1 states, we
predict a significant suppression of the product of inferred quadrature
variances below the Heisenberg uncertainty limit, implying strong EPR
entanglement. However, such EPR entanglement is lost when the collisions are
initiated in the presence of a small (currently undetectable) thermal
population n_{th} in the m_{F}=+-1 states. For condensates containing 150 to
200 atoms, we predict an upper bound of n_{th}~1 that can be tolerated in this
experiment before EPR entanglement is lost.
