Hawaii appears to have the strictest implementation in the country:
> Starting May 11, fully vaccinated individuals in Hawaii who uploaded their proof of vaccination to the state's "Safe Travels" system were allowed to travel inter-county without pre-travel testing and quarantine restrictions.
NY has a state-sponsored app that businesses can choose to require:
> New York has introduced a government-sponsored digital vaccine passport program called the Excelsior Pass, according to the AP. The smartphone app shows whether someone has been vaccinated or recently tested negative for COVID-19. At least some sports and performance venues, such as Madison Square Garden and Yankee Stadium, have used Excelsior Pass to prove vaccination