6. Mixed unitary channels [8 points].

A channel is mixed-unitary if it can be expressed in terms of Kraus operators Ao,

, Am-1

that are of the form Ak = √Pk Uk, where Uo,...,Um-1 are unitary and (Po... Pm-1) is

a probability vector.

Consider the one-qubit channel that maps every 2×2 density matrix to the density matrix

[1/2]. Show that this is a mixed-unitary channel by exhibiting four Kraus operators,

A0, A1, A2, A3, for it that are in the form of a mixed-unitary channel.