Revisiting the optimal detection of quantum information

In 1991, Peres and Wootters wrote a seminal paper on the nonlocal processing of quantum information. We return to their classic problem and solve it in various contexts. Specifically, for discriminating the "double trine" ensemble with minimum error, we prove that global operations are more powerful than local operations with classical communication (LOCC). Even stronger, there exists a finite gap between the optimal LOCC probability and that obtainable by separable operations (SEP). Additionally we prove that a two-way, adaptive LOCC strategy can always beat a one-way protocol. Our results demonstrate "nonlocality without entanglement" in two-qubit pure states.