Miza Rahaman, Department of Pure Mathematics, University of Waterloo
"Multiplicative Properties of Quantum Channels"
In this talk I will present a recently undertaken study on multiplicative behaviour of trace preserving and completely positive maps acting on matrix algebras. Such maps are called quantum channels in information theory. It will be shown that any arbitrary unital quantum channel, when restricted to a specific domain, behaves as an automorphism. This domain captures certain spectral properties of the channel and is also useful in determining the asymptotic behaviour of the given channel. The concept of 'multiplicative index' of a channel will be introduced and some examples will be given to compute this index. Some connections to the non-commutative Perron-Frobenius theory will be made with the study of multiplicative properties of channels.
MC 5417