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How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. Spin and the Kraus-operator geometry of SL(2,C)

Thursday September 9, 2021
3:30 pm

 Presenter:  Carl Caves (UNM)
 Series:  CQuIC Seminars
 Abstract:  I will discuss how to perform the measurement of the spin-coherent-state POVM by making weak, continous isotropic measurements of the three spin components. Starting from the standard approach to weak, continuous measurements, the analysis becomes distinctive by focusing on the Kraus operators that develop over the course of the continuous measurements, analyzing their evolution by path integrals, diffusion equations, and stochastic differential equations. The Kraus-operator-centric approach reveals the representation-independent geometry of the group SL(2,C) in which the Kraus operators move. The spin coherent states make up a 2-sphere phase space on the boundary of the space of Kraus operators. The talk, ultimately, is not about the destination, measurement of spin coherent states, but rather the journey through the space of Kraus operators and what that teaches about quantum mechanics. Hang on for the ride.

I will briefly indicate how all this can be generalized to phase-space correspondences for any compact semi-simple Lie group and sketch how the vision that all of physics, classical and quantum, occurs on (generally curved) phase spaces opens up new avenues for research.

This work was carried out with Christopher S. Jackson.
 Host:  Ivan Deutsch
 Location:  PAIS-2540, PAIS

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