Optimal quantum learning of a unitary transformation
- QUIT Group, Dipartimento di Fisica 'A. Volta' and INFN Sezione di Pavia, via Bassi 6, I-27100 Pavia (Italy)
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 with 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.
- OSTI ID:
- 21413293
- Journal Information:
- Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032324; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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