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Optimal Quantum Learning of a Unitary Transformation by Bisio, A.; Chiribella, G.; D'Ariano, G. M.; Facchini, S.; Perinotti, P. is a scholarly article available to read on EtoBox.

What is Optimal Quantum Learning of a Unitary Transformation about?

We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine), and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a "measure-and-rotate" retrieving. Differing from the case of quantum cloning, where the incoherent "measure-and-prepare" strategies are typically suboptimal, in the case of learning the "measure-and-rotate" strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the "measure-and-rotate" strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication.

Author

Bisio, A.; Chiribella, G.; D'Ariano, G. M.; Facchini, S.; Perinotti, P.

Published

2009

Language

EN