Quantum Probability Team 
Workshops and Seminars
(for other seminars related to Quantum Information in the
"Città Studi" area see also Open Systems & Quantum Information Seminars)
17  01  2019 ore 11:30  Aula Consiglio VII piano Alessandro Toigo (Politecnico di Milano): QUANTUM INCOMPATIBILITY WITNESSES We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement setup after Alice has announced him the chosen ensemble (premeasurement scenario), or he is forced to perform the measurement before of Alice’s announcement (postmeasurement scenario). In the latter case, he can only postprocess his measurement outcome when Alice’s extra information becomes available. We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task within the premeasurement scenario. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve Bob’s probability of guessing the correct state. The gap between the guessing probabilities with pre and postmeasurement information is thus a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme.

