Critical altitude
Turbochargers increase a piston engine's critical altitude, which is the maximum altitude at which an engine can maintain its full, rated horsepower. Because the maximum horsepower of a normally aspirated (nonturbocharged) engine is achieved in standard, sea level conditions, sea level is this engine's critical altitude.
From AOPA (USA) Flight Training magazine website
Quote: "Even most turbines can't be started above 10000 feet."
I would think that the PT6 qualifies as "most turbines" - this is the airstart envelope for a PT6-66D:
