  This document focuses on translating various information-theoretic measures
of distinguishability for probability distributions into measures of distin-
guishability for quantum states. These measures should have important appli-
cations in quantum cryptography and quantum computation theory. The results
reported include the following. An exact expression for the quantum fidelity
between two mixed states is derived. The optimal measurement that gives rise to
it is studied in detail. Several upper and lower bounds on the quantum mutual
information are derived via similar techniques and compared to each other. Of
note is a simple derivation of the important upper bound first proved by Holevo
and an explicit expression for another (tighter) upper bound that appears
implicitly in the same derivation. Several upper and lower bounds to the quan-
tum Kullback relative information are derived. The measures developed are also
applied to ferreting out the extent to which quantum systems must be disturbed
by information gathering measurements. This is tackled in two ways. The first
is in setting up a general formalism for describing the tradeoff between
inference and disturbance. The main point of this is that it gives a way of
expressing the problem so that it appears as algebraic as that of the problem
of finding quantum distinguishability measures. The second result on this theme
is a theorem that prohibits "broadcasting" an unknown (mixed) quantum state.
That is to say, there is no way to replicate an unknown quantum state onto two
separate quantum systems when each system is considered without regard to the
other. This includes the possibility of correlation or quantum entanglement
between the systems. This result is a significant extension and generalization
of the standard "no-cloning" theorem for pure states.
