1207.5420 (Anna Jencova)

Extremal measurements on quantum channels    [PDF]

Anna Jencova

A measurement on a section K of the set of states is defined as an affine map from K to the set of probability measures on the set of outcomes. Such measurements correspond to equivalence classes of so-called generalized positive operator valued measures (POVMs). A special case is the set of all channels B(H) to B(K), for finite dimensional Hilbert spaces H and K, which can be identified with a section of the set of states on B(K\otimes H). The corresponding generalized POVMs are the so-called quantum 1-testers. We find extremality conditions for measurements on K. Moreover, we characterize generalized POVMs such that the corresponding measurement is extremal. These results are applied to the set of channels. We find explicit extremality conditions for two outcome measurements on qubit channels and give an example of an extremal qubit 1-tester such that the corresponding measurement is not extremal.

View original: http://arxiv.org/abs/1207.5420