Simulating quantum operations with mixed environments

We study the physical quantum resources required to implement general quant um operations, and provide bounds on the minimum possible size which an env ironment must be in order to perform certain quantum operations. We prove t hat contrary to a previous conjecture, not all quantum operations on a sing le qubit can be implemented with a single-qubit environment, even if that e nvironment is initially prepared in a mixed state. We show that a mixed sin gle-qutrit environment is sufficient to implement a special class of operat ions, the generalized depolarizing channels. [S1050-2947(99)04107-4].