Quantum Measurement and Continuous Markov Processes Mini-Course, Oct 27 - Dec 11, 2025

This series is a crash course introduction to a handful of advanced topics designed to tackle the general problem of how to engineer Positive Operator-Valued Measures (POVMs) using observable building blocks, the so-called Instrument Manifold Program. This program emerged from a recent fundamental breakthrough: how to realize the measurement of a spin’s direction, a.k.a. the spin-coherent-state POVM, a spherical set of outcomes analogous to the well known coherent-state POVM of the standard phase plane.

Mostly ignore the Introduction content of the Oct 27 lecture (up to 14:14). The content and direction of the course evolved such that different portions of the “Old Schedule” (at 0:27) were covered. The schedule on this page has been corrected and now accurately reflects the content of the lectures.

The “Supplements” on Oct 30 and Nov 06 are actually just Lectures.

Outline:
Oct 27: The Planimeter and the Weyl-Heisenberg Group of Kinematic Transformations
Oct 30: The Planimeter and the Weyl-Heisenberg Group of Canonical Transformations
Nov 03: No Class
Nov 06: Measuring Instruments, Indirect Quantum Measurement, and Positive Gaussian Kraus Operators
Nov 10: Gaussian Channels, Gaussian Random Unitaries, and Sequential Measurements
Nov 13: Wiener Increments and the Ito Rules
Nov 17: No Class
Nov 20: General Gaussian Kraus Operators, Lindblad Operators, and Diffusive Measurement
Nov 24: The Markov Property and The Central Limit Theorem
Nov 27: Instrumental Groups, von Neumann Measurement, and Diffusive Heterodyne
Dec 01: No Class
Dec 04: The Stratonovich Product, The Maurer-Cartan Stochastic Differential, and Indirect Homodyne
Dec 08: The Kraus-Operator Density and The Fokker-Planck-Kolmogorov Equation of a Diffusive Measurement
Dec 11: Simultaneous Diffusive Measurements of Non-Commuting Observables and the Instrument Manifold Program

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo (Exception - November 27 in Space Room, 4th Floor)

Registration: Please sign-up here: https://forms.office.com/r/dEA4EUq0CU

Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].