  Dirac equation describes the dynamics of a relativistic spin-1/2 particle
regarding its spatial motion and intrinsic degrees of freedom. Here we adopt
the point of view that the spinors describe the state of a massive particle
carrying two qubits of information: helicity and intrinsic parity. We show that
the density matrix for a gas of free fermions, in thermal equilibrium,
correlates helicity and intrinsic parity. Our results introduce the basic
elements for discussing the spin-parity correlation for a Fermi gas: (1) at the
ultra-relativistic domains, when the temperature is quite high, $T > 10^{10}\
K$, the fermions have no definite intrinsic parity (50% : 50%), which is
maximally correlated with the helicity; (2) at very low temperature, $T \approx
3 \ K$, a unique parity dominates (conventionally chosen positive), by
$10^{20}$ to $1$, while the helicity goes into a mixed state for spin up and
down, and the quantum correlation decoheres. For the anti-fermions we get the
opposite behavior. In the framework of quantum information, our result could be
considered as a plausible explanation of why we do accept, as a fact
(consistent with the experimental observation), that fermions (and
anti-fermions), in our present epoch of a cool universe, have a unique
intrinsic parity. The framework for constructing spin-parity entangled states
is established.
