Actually, I think the channel is not extremal because I suspect you are misquoting the Landau-Streater result. So I will state it here.
To be precise, for anyone unfamiliar with the field, a quantum channel is a trace-preserving, completely-positive linear map on density matrices (positive semidefinite matrices with unit trace), of potentially different sizes. A basic theorem in quantum information says that every quantum channel from mtimesm-dimensional to ntimesn-dimensional density matrices can be written in Kraus form:
rhomapstosumNi=1AirhoAdiagger,textforlinearoperatorsAkcolonmathbbCmtomathbbCntextsatisfyingsumkAdkaggerAk=Im.
It is easy to show that the set of quantum channels between systems of fixed dimension is convex. It also easy to show that the set of channels that map frac1mIm to a fixed density matrix sigma is convex. Now the theorem of Landau-Streater says that if m=n, a channel with Kraus form as above is extremal in this latter set if and only if the N2 linear operators AdiaggerAjoplusAjAdaggeri (of size 2mtimes2m) are linearly independent. It seems you have instead been working with mtimesm matrices. But I think that even if you were to continue and apply the theorem correctly, you would only prove or disprove extremality in the convex subset of unital channels, i.e. those for which frac1mI is a fixed point. So potentially you could strengthen Ben-Or's conclusion by showing non-extremality in this subset, or otherwise you might conclude extremality there, which would tell you nothing about extremality in the entire set of channels.
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