Abstract.
Quantum mechanics takes place in a complex projective space, the Hilbert space. By viewing this space from a geometric perspective new perspectives on quantum theory can be gleamed, and interesting connections to topology and quantum sensing/parameter estimation (metrology) can be found.
In the first part of this talk, I will introduce this geometric perspective on quantum mechanics, defining the quantum metric and highlighting the analogy of this construction to general relativity. In the second part I will connect these geometric ideas to problems from parameter estimation, by reinterpreting the metric as a quantum version of the Fisher information, which is the crucial quantity in metrology, the science of measurements and sensing. Finally, time allowing, I will discuss some recent results combining geometry, topology and sensing, as discussed in my preprint arXiv:2501.16428.
(The slides will be available here)