Dynamics of an entangled pair of spin-$\frac{1}{2}$ particles under correlated random magnetic fields

The dynamics of a maximally entangled pair of spin-$\frac{1}{2}$ particles is obtained in the presence of random magnetic fields which are correlated. The two spin-$\frac{1}{2}$ particles are assumed to be maximally entangled initially and are then disturbed by the magnetic fields modeled as Gaussian vector random processes whose corresponding spatial components are correlated. The dynamics is derived in terms of the joint density matrix of the entangled pair using the ideas of stochastic calculus, from which the steady-state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix represents a state of (partial) disentanglement.