  Taking a system of two coupled qubits described by a X-shaped state and
interacting through an anisotropic Heisenberg XY interaction, we examine the
evolution of quantum entanglement and a few quantum correlations beyond
entanglement, local quantum uncertainty and measurement-induced nonlocality,
under the environmental decoherence both for zero and finite temperatures. The
relation between concurrence and log negativity as two well-known quantifiers
of entanglement is argued. It will be proven that measurement-induced
nonlocality equals correlated coherence. The interaction of qubits with the
environment causes quantum entanglement to suddenly die for independent qubits,
but other correlations do not experience this phenomenon. The time of
entanglement sudden death is calculated analytically for zero temperature,
while numerically for finite temperatures. Contrary to its usual destructive
role, the environment plays a constructive role in some situations, inducing
quantum correlations even when the initial quantum correlations are zero. The
steady state quantum correlations, being independent of the initial state, are
found to remain all non-zero for low, finite temperatures. It is found that
quantum correlations beyond entanglement are more robust against temperature
than entanglement. The zero-temperature steady state exhibits less local
quantum uncertainty than the other correlations.
