www.alphadictionary.com

Read in the NYTimes:
"Terry Sullivan, the executive director of the White House Transition Project, a nonpartisan organization that tracks the pace of appointments [said] 'The federal government is quantum times larger than the largest American corporation. It puts Exxon Mobil in the shade. It is a reflection of naïveté about how big the U.S. government is.'”

I quess Mr Sullivan doesn't know that a "quantum" is defined as "the smallest discrete quantity of some physical property that a system can possess"

So a "quantum increase" would be just a tiny bit larger and the result of multiplying a large number (the largest American corporation) by a tiny fraction of itself (its quantum) will be a number much smaller than the original large number.

I guess the quotation reflects a certain naivete about meaning of the words he uses.

I agree, especially in the usage in your quote. But I believe I have heard the expression "quantum shift" in the sense of a radical paradym change comparable to that in physics when quantum mechanics came into play. Results and their implications still roil scientists today with the wierdest consequences immaginabke!

We also have the concept of a quantum leap forward.

There are several meanings accepted for this word, so both great and small are correct.