Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal quantum learning of a unitary transformation   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.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol