Beating Shannon requires BOTH efficient adversaries AND non-zero advantage

In this note we formally show a well known (but not well documented) fact that in order to beat the famous Shannon lower bound on key length for one-time-secure encryption, one must simultaneously restrict the attacker to be efficient, and also allow the attacker to break the system with some non-zero (i.e., negligible) probability. Our proof handles probabilistic encryption, as well as a small decryption error.