In this video, I talk about the task of state discrimination. Given two states chosen from a probability distribution, I address the question of what is the maximum probability of success of guessing the state correctly. It turns out that such a question has a closed-form expression provided by the Holevo-Helstrom theorem. I discuss the theorem and how to prove it. The idea is to frame the trace norm or trace distance between two states as an optimization problem. I discuss this in detail and also talk about what the optimizer is.
