A cross reality system that provides an immersive user experience shared by multiple user devices by providing quality information about a shared map. The quality information may be specific to individual user devices rendering virtual content specified with respect to the shared map. The quality information may be provided for persistent coordinate frames (PCFs) in the map. The quality information about a PCF may indicate positional uncertainty of virtual content, specified with respect to the PCF, when rendered on the user device. The quality information may be computed as upper bounding errors by determining error statistics for one or more steps in a process of specifying position with respect to the PCF or transforming that positional expression to a coordinate frame local to the device for rendering the virtual content. Applications running on individual user devices may adjust the rendering of virtual content based on the quality information about the shared map.