Optimum unambiguous identification of d unknown pure qudit states

We address the problem of unambiguously identifying the state of a probe qudit with the state of one of d reference qudits. The reference states are assumed pure and linearly independent but we have no knowledge of them. The state of the probe qudit is assumed to coincide equally likely with either one of the d unknown reference states. We derive the optimum measurement strategy that maximizes the success probability of unambiguous identification and find that the optimum strategy is a generalized measurement. We give both the measurement operators and the optimum success probability explicitly. Technically, the problem we solve amounts to the optimum unambiguous discrimination of d known mixed quantum states.Comment: A reference has been included and a sign error has been corrected that propagated and affected the final result and is unfortunately also present in the printed journal versio

Compactification of a map which is mapped to itself

We prove that if $T: X \to X$ is a selfmap of a set $X$ such that \bigcap \{T^{n}X: n\in N}\} is a one-point set, then the set $X$ can be endowed with a compact Hausdorff topology so that $T$ is continuous.Comment: 5 page