Application of the EWL protocol to decision problems with imperfect recall

We investigate implementations of the Eisert-Wilkens-Lewenstein scheme of playing quantum games beyond strategic games. The scope of our research are decision problems, i.e., one-player extensive games. The research is based on the examination of their features when the decision problems are carried out via the EWL protocol. We prove that unitary operators can be adapted to play the role of strategies in decision problems with imperfect recall. Furthermore, we prove that unitary operators provide the decision maker possibilities that are inaccessible for classical strategies.