We get the above question enough that it is probably worth addressing in a blog post. Unless we are talking about federal agents (who can operate throughout the country), the arrest authority of police detectives is typically limited to their home jurisdiction. For example, a Spokane police detective is typically only commissioned within the city of Spokane. It is possible that a detective is "cross commissioned" with a neighboring agency, or it is possible for him or her to act elsewhere in Washington under the Mutual Aid Act. 
However, that same detective doesn't have any special authority to arrest another person in another state. When detectives seek to arrest a person in another state, they will reach out to the police in the local jurisdiction for an "agency assist." Detectives are allowed to travel throughout the country to interview or talk to anyone they choose. There is no license or special authority required for that. However, it is customary for the police to notify the local jurisdiction they are visiting as a matter of courtesy. Often times a local police officer will accompany the detectives from the visiting jurisdiction for any interviews they conduct. Keep in mind that while police visiting from a different state don't have the arrest authority of the local police, they still do have the power to make a citizen arrest, i.e. at least in Washington they can arrest for a felony or a breach of the peace that is committed within their presence.
