For deeper understanding of quantum non-local correlations a new path integral \textit{real--time} quantum dynamics approach has been developed and applied to the Monte Carlo simulation of the decoherence of pair entangled states in many--body systems in the framework of the ``replica trick''. Calculations have been carried out for the Heisenberg--Wigner path integral representation of the entangled state correlation function (ESCF) in the modified unified electron gas model as example. The Wiener--Khinchin transformation of ESCF has been applied to random paths in path integral allowing for the Monte Carlo simulation of ESCF. Presented results include the spin--resolved radial distribution functions, the ESCF and estimations of the decoherence time of the entangled electron pairs due to thermalization and interparticle interaction.