The Heritage Foundation seeks to answer this question by producing their beautifully rendered multi-dimensional Index of Economic Freedom. From this, they've produced this hyperbolic graph that makes it appear indisputable that economic freedom and economic prosperity are locked:

Upon inspection of what the individual dimensions are, though, they seem to represent economic freedoms that would get a tycoon excited. Never mind the economic freedom of a group of employees to negotiate their own wage, that's irrelevant to the "Labor Freedom" dimension.

Also, the case of China's recent growth prompted me to do my own research, and see whether this graph is a causation-vs-correlation mix-up. I went through Wikipedia's List of countries by GDP growth 1990-2007, took the countries that had a GDP of over $100 billion (since a small country could potentially manage a few large corporations and make more than $10 billion), and graphed their economic freedom vs. their growth. As you can see, the relationship isn't quite so clear:

Apparently this same idea and a similar graph is mentioned in Jeffrey Sachs's The End of Poverty: Economic Possibilities.