We present a recursive quantum mechanical model for the fragmentation of a string stretched between a quark and an antiquark with entangled spin states. The quarks are assumed to be produced in the e+e- annihilation process via the exchange of a virtual photon and the correlations between their spin states are described by a joint spin-density matrix. The string fragmentation process is formulated at the amplitude level by using the splitting matrices of the recent string+3P0 model of polarized quark fragmentation with pseudoscalar and vector meson emissions and accounts for the systematic propagation of the spin correlations in the fragmentation chain. The model is formulated as a recursive recipe suitable for a Monte Carlo implementation. It reproduces the expected angular correlation, due to the Collins effect, between back-to-back pseudoscalar and/or vector mesons. For the latter, this correlation also involves the momenta of the decay products. We use the model for studying the sign of the Collins asymmetry for back-to-back vector and pseudoscalar mesons.
