Wednesday, January 20, 2016 — 11:00 AM EST
Daniel Puzzuoli| Applied Math, University of Waterloo
Ancilla dimension for optimal channel discrimination
In this seminar we will discuss the role of the ancilla dimension in channel discrimination problems. We will review state and channel discrimination games and present what is known about optimal success probabilities in these games, with emphasis on role of the dimension of the ancilla system. It is well known that an ancilla with dimension equal to the input dimension of the channels being discriminated is always sufficient for optimal channel discrimination. A natural question then, is when the output dimension is smaller than the input dimension, is optimal discrimination always possible when the ancilla has dimension equal to that of the output system? We will show that the answer is no by providing a family of counter examples. Interestingly, this family contains instances with arbitrary finite gap between the input and output dimensions, and also has the property that, even with arbitrary finite gap, an ancilla of any dimension less than the input dimension is insufficient for optimal discrimination. Future directions and numerical investigations will also be discussed.