First you should realize that "quantum" means very, very small.
1. Physics
a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents.
an analogous discrete amount of any other physical quantity, such as momentum or electric charge.
Physiology
the unit quantity of acetylcholine released at a neuromuscular junction by a single synaptic vesicle, contributing a discrete small voltage to the measured end-plate potential.
2. Legal
a required or allowed amount, especially an amount of money legally payable in damages.
Since 'quantum' anything is a broad term, the quantum 'whatever' in your story needs to have a focus.
You can search the web for examples of quantum in application
Being that it is the realm of the very small, any quantum 'effect' you wish to use will need to associate with the very small.
However, it is possible for a quantum related action to affect the larger scale objects.
Changing a quantum value could change all the atomic values related to an object.
Quantum manipulation of matter could be associated with advanced nanotechnology.
Also time travel and teleportation.
It will affect the matter of an object but not the subsequent matter interactions with other matter.
Entanglement principles could allow for long distance teleportation but a 'station' would be required at the destination.
Quantum teleportation has already been done.
Researchers in China have teleported a photon from the ground to a satellite orbiting more than 500 kilometers above.
www.technologyreview.com
View attachment 13911
Ref:
arxiv.org/abs/1707.00934: Ground-to-satellite quantum teleportation
Additionally, you might suggest an AI has quantum synapse.
Right now, the teleportation experiments are limited to the sending of information.
Its still an early science.
There is no reason to think it wouldn't lead to matter teleportation with more research time?
Without knowing the application in which you wish to include quantum in your story, any responses will be limited to general feedback.