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

Abstract

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 orderpreserving quantum operation.

Keywords

• partial b-metric space
• order-preserving mapping
• quantum operation
• fidelity of quantum state
• bloch vector