Abstract
In the simplest problems of quantum communication, Alice transmits one of two quantum states, with equal probabilities, to Bob's receiver, modeled by a positive-operator-valued measure (POVM); one seeks the POVM that is optimal according to one or another criterion. We discuss four such criteria, the first three of which lead to distinctive types of POVM. By introducing a reciprocal basis for the state vectors, we shorten the derivations of known results for the two most popular criteria. A new optimization problem defined by a third criterion, intermediate between the first two, is formulated and solved. Then we turn to a fourth criterion, that of minimizing Bob's Renyi entropy for an arbitrary order α. Depending on the value of α and the separation of Alice's states, the POVM that minimizes Bob's entropy can be any of the preceding three types.
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