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How Difficult is it to Prepare a Quantum State?
1Los Alamos National Laboratory, Theoretical Division, P.O. Box 1663 Los Alamos, New Mexico 87545, USA and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA.
Abstract:
Consider a quantum system prepared in an input state. One wants to drive it into a target state. Assuming classical states and operations as free resources, I identify a geometric cost function which quantifies the difficulty of the protocol in terms of how different it is from a classical process. The quantity determines a lower bound to the number of commuting unitary transformations required to complete the task. I then discuss the link between the quantum character of a state preparation and the amount of coherence and quantum correlations that are created in the target state.
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