Distinguishing classically indistinguishable states and channels

Karol Zyczkowski (Jagiellonian University)

RESUMEN: For a given classical n-point probability vector p we describe the set of pure quantum states of order n which decohere to p. In particular, we analyze the question, how many mutually orthogonal quantum states decohere to the given classical state p. In other words, we ask, how many quantum states can be perfectly distinguished, even though their classical counterparts are identical and thus indistinguishable. A similar problem can also be posed for channels: For a given classical map corresponding to a stochastic transition matrix T we look for a quantum channel, which induces the same classical transition matrix T, but is "more coherent". To quantify the coherence of a channel we measure the coherence of the corresponding Jamiolkowski state. It is shown that a classical transition matrix T can be coherified to a reversible unitary dynamics if and only if T is unistochastic.