  The quantum entanglement measure is determined, for the first time, for a
collection of spin-1/2 arranged in a infinite chain with finite temperature and
applied to a single-crystal \beta-\mathrm{T_eVO_4}. The physical quantity
proposed here to measure the entanglement is the distance between states by
adopting the Hilbert-Schmidt norm. We relate the distance between states with
the magnetic susceptibility. The decoherence temperature, above which the
entanglement is suppressed, is determined for a system. A correlation among
their decoherence temperatures and their respective exchange coupling constants
is established, moreover, it is conjectured that the exchange coupling protects
the system from decoherence as temperature increases.
