Fixed point theorem in a partial b-metric space applied to quantum operations

Introduction/purpose: A fixed point theorem of an order-preserving mapping on a complete partial b-metric space satisfying a contractive condition is constructed. Methods: Extension of the results of Batsari et al. Results: The fidelity of quantum states is used to construct the existence of a fixed quantum state. Conclusions: The fixed quantum state is associated to an order-preserving quantum operation.