Economizing Nonlocal Resource in Two-Way Remote Preparations of Inequivalent Quantum States Under a Common Control

A recently proposed protocol for two parties to securely and simultaneouslyexchange inequivalent quantum states under the same control of a third party[Int. J. Theor. Phys. (2020);https://doi.org/10.1007/s10773-020-04657-0] is revisited. It shown inthis paper that required tasks are equally well accomplished with anonlocal resource which greatly economized by rationally exploiting localresources. Furthermore, nonlocal appropriatelocal operations on local resources also allows exchanging inequivalentstates other than those previously considered.