Matrix N-dilations of quantum channels

Abstract

We study unital quantum channels which are obtained via partial trace of a * -automorphism of a finite unital matrix * -algebra. We prove that any such channel, q, on a unital matrix * -algebra, A, admits a finite matrix N −dilation, αN , for any N ∈ N. Namely, αN is a * -automorphism of a larger bi-partite matrix algebra A ⊗ B so that partial trace of M -fold self-compositions of αN yield the M -fold self-compositions of the original quantum channel, for any 1 ≤ M ≤ N . This demonstrates that repeated applications of the channel can be viewed as * -automorphic time evolution of a larger finite quantum system.