Classical arguments predict that the quark and the antiquark of a pair created during string fragmentation are both transversely polarized in the direction of \hat z \times \vec q_T, where z is the direction of the pull exerted by the string on the antiquark and \vec q_T (-\vec q_T) is the transverse momentum of the quark (antiquark). The existence of this effect at the quantum-mechanical level is investigated by considering two analogous processes involving the tunnel effect in a strong field: (1) dissociation of the positronium atom (2) electron pair creation. In case (1) the positronium is taken in the 3P_0 state to simulate the vacuum quantum numbers J^PC = 0^++. Using the nonrelativistic WKB method, the final electron and positron are indeed found to be transversely polarized along \hat z \times \vec p_T. On the contrary, case (2), treated with the Dirac equation, shows no correlation between transverse polarization and transverse momentum both when the field is uniform and when it depends on z and t. The pair is nevertheless produced in a triplet spin state. The difference between these two results and their relevance to transverse spin asymmetry in inclusive reactions is discussed.