Physics Seminar
Date: Thursday, 06 March 2025
Time: 3.30 PM
Venue: Lecture Hall 2
Geometry of pure Quantum states as revealed by weak measurements
N D Hari Dass
Retired Senior Faculty, Institute of Mathematical Sciences, Chennai, Chennai.
06-03-25

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Abstract

In this talk I discuss how state spaces in quantum mechanics are probed by measurements. I will be restricting myself only to pure states. A simple analysis shows that they are always even dimensional(not true for mixed states). So in principle these could be complex manifolds. In fact, mathematicians have shown that not only are they complex mani- folds, they are also the so called K¨ahler manifolds. After discussing the novel measurement schemes introduced by Aharonov and coworkers, called ’Weak Measurements’ and ’Weak value measurements’, I will show how the weak values provide natural complex coordinates for the projective Hilbert spaces. I will explicitly work out all the geometrical details for the spin-1/2(qubit) and spin-1(qutritt) cases.