There's currently no definitive, notable reduction in transmission due to vaccination (there are published anecdotes/thories -- but nothing definitive), due in large part to the relative newness of the strain(s), and therefore lack of historical data. There are excellent papers in Science, Nature, and of course other peer-reviewed academic journals.
Sharing this link just as a resource (there are many) where this is discussed:
A Facebook post, shared hundreds of times since Jan. 15, claims that the COVID-19 vaccine does not prevent transmission of the disease, meaning vaccinated people will effectively become “silent spreaders”. It uses this as an argument against introducing health passports...
www.reuters.com
Conclusion:
"There is no conclusive evidence to claim COVID-19 vaccines do not prevent people spreading the disease. Scientists are not yet sure of how the vaccine affects transmission – and this is currently undergoing research. People are still required to follow restrictions even after vaccination to account for this uncertainty."