DYNAMICS OF ENTANGLED PAIR OF SPIN-1/2 PARTICLES IN THE PRESENCE OF RANDOM MAGNETIC FIELDS

Abstract

The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the identical, independent, correlated random magnetic fields is studied. The dynamics of the pure joint state of the pair is derived using stochastic calculus. In case of identical fields, an ensemble of such pure states are combined using the modified spin joint density matrix and the joint relaxation time is obtained for the pair of spin-1/2 particles. These dynamics can be interpreted as special kind of correlations involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles. In case of independent random magnetic fields, the dynamics are obtained by considering a pure joint state of entangled spin-1/2 particles. The disentanglement time defined as the time taken for the particles to become disentangled, is obtained. In case of correlated random magnetic fields, the dynamics of a maximally entangled pair of spin-1/2 particles are derived in terms of the joint density matrix of the entangled pair from which the steady state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix in this case represents a state of (partial) disentanglement. In other words, there is a persistent entanglement in case of correlated field disturbances.