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Coherent Measuring Processes and the Differential Geometry of Measuring Instruments

Thursday September 15, 2022
3:30 pm


 Presenter:  Chris Jackson (Sandia)
 Series:  CQuIC Seminars
 Abstract:  Noncommuting observables can be measured simultaneously weakly and therefore simultaneously continually.
The simplest such simultaneous continual observations culminate into the generalized-coherent-state measurements.
With the discovery of how the spin-coherent-state measurement can be performed, I've had to develop the theory of simultaneous continual observation beyond the theory of population master equations (which appears to have dominated the discussion of quantum measurement for almost 50 years now.)
Fundamentally, instruments have a physical reality independent of the states that may stimulate their senses.
To bring forward this principle of instrument independence for continual observations, I designed what I’ve been calling the Kraus-operator density of a principal unraveling.
Under this design, continual observation translates to the mathematical problem of a Kraus-operator density diffusing over a differentiable manifold.

What I'll be showing you guys is how all this looks for the apparently simple problem of continually observing the canonical Q and P.
There are two distinct ways to continually observe Q and P, related to a work by Barchielli (1982) and a work by Wiseman (1993).
Both continual observations translate to a specific Kraus-operator diffusion process in a 7-dimensional manifold:
2 for the pre-measurement phase space, 2 for the post-measurement phase space, 1 for the operator rank, and 2 further renormalization dimensions.
Explicitly solving for the Kraus-operator density, there are two very remarkable features:
1 - the Planck Distribution follows and thus demonstrates that simultaneous observation is a fundamental alternative to the usual quantization of the energy.
2 - Renormalization Group equations appear to follow and thus the time of a simultaneous observation appears to be a fundamental alternative to the usual regularization schemes of perturbation theory.
 Host:  Carlton Caves
 Location:  PAIS-2540, PAIS

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