An inequality for quantum fidelity
Abstract
Quantum fidelity is an important quantity in quantum information theory and quantum chaos theory. It is a distance measure between density matrices which are considered as quantum states. Although it is not a metric, it has many useful properties that can be used to define a metric on the space of density matrices. In this note we prove a parameterized inequality for quantum fidelity. As a consequence, for quantum states A and B such that A - B 1 ≤ 64/ 81 , our result is a refinement of the well-known Fuchs-van de Graaf ’s inequality.