Minimal Entropy of States Emerging from Noisy Channels

Mary Beth Ruskai

In quantum communication, a noisy channel is represented by the action of a stochastic (i.e., completely positive trace-preserving) map on the set of density matrices. For unital stochastic maps acting on 2 x 2 matrices, entangling states which emerge with minimal entropy cannot decrease the entropy below that attainable from product states. We will explain why this result provides strong evidence for the conjecture that the minimal entropy of the product of any two stochastic maps is additive. We will explain why it suggests that, for unital maps on 2 x 2 matrices, the Holevo capacity is additive, achieved by orthogonal States, and equal to the Shannon capacity. If time permits, some comments on the minimal entropy and Holevo capacity of non-unital maps will also be discussed.

created Thu Mar 2 11:38:45 PST 2000