  We consider quantum correlations in a spin-1/2 open chain of $N$ nodes with
the XY Hamiltonian using different bases for the density matrix representation
and the initial state with a single polarized node. These bases of our choice
are following: (i) the basis of eigenvectors of the fermion operators; this
basis appears naturally through the Jordan-Wigner transformation (this
representation of the density matrix is referred to as the
$\beta$-representation), (ii) its Fourier representation ($c$-representation of
the density matrix) and (iii) the basis of eigenvectors of the operators
$I_{jz}$ (the $z$-projection of the $j$th spin, $j=1,...,N$). Although for the
short chains (a few nodes) the qualitative behavior of the entanglement and the
discord are very similar (the difference is quantitative), this is not valid
for longer chains ($N\gtrsim 10$). In this case, there are qualitative and
quantitative distinctions between the entanglement and the discord in all three
cases. We underline three most important features: (i) the quantum discord is
static in the $\beta$-representation, where the entanglement is identical to
zero; (ii) in the $c$-representation, the concurrence may be non-zero only
between the nearest neighbors (with a single exception), while the discord is
nonzero between any two nodes; (iii) there is so-called "echo" in the evolution
of the discord, which is not observed in the evolution of the concurrence.
Using different bases, we may choose the preferable behavior of quantum
correlations which allows a given quantum system to be more flexible in
applications.
