Abstract: We introduce the ◇2p roducts by considering two physical quantities ( namely, the concurrence and fidelity) , which p lay an important role in quantum computation and quantum information. Then by comparing ◇2 p roduct with the sequential p roduct, we give some algebraic p roperties of ◇2p roducts and some counter examp les. Finally, we obtain a characterization of trans 2formations that p reserve concurrence or fidelity between different Hil2 bert spaces.