Am I entitled to any benefit by implementing an idea from my professor's published paper?
This is a perfect situation for you to suggest that if possible you would like to get started on a career that includes publication of scholarly articles, either alone or in collaboration with the prof. Ask him if this project is a good vehicle for this. It assumes either the implementation or an extension of the original paper is valid for publication, of course. You might wind up a big winner. He will, in any case, likely consider you for a future project if this one doesn't seem right to him. There is little to lose. 

Don't ask him for a gimme. Ask for collaboration and help in learning how to develop and write for publication. 

There are two additional thoughts. Maybe he just didn't think of it, so your approach might wake him up to the possibility. And also, he may put your name around to other faculty who might be willing also. Just expressing your interest can start a lot of wheels turning.