| Distances between quantum states |
October, 26 (2007) at 3:30pm Pedro Walter Lamberti Encountering two quantum states, one might ask how similar they are. Clearly one can think of ways to understand `similar' that would make this question relevant in quantum information processing. One reformulation of the question could be: How well can we distinguish between the two states, with the aid of a measurement? Orthogonal states are one-shot distinguishable - it is possible to measure just once to know the state. But for given non-orthogonal states, there is no measurement that will discriminate between the states with certainty. Then we can ask for the measurement that will be the most advantageous, in a statistical sense, for distinguishing them. For every measurement, the two states give two probability distributions for the outcomes. To distinguish between the states we need to distinguish between the probability distributions. In this seminar we review the main properties of some distances between probability distributions and their extension as distances between density operators. |