A Bayesian Probability Calculus for Density Matrices
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29·
summary
Defines a Bayesian calculus where probabilities are density matrices and derives joint, conditional and marginal rules using quantum relative entropy and partial trace operations. Updates use a matrix-log/exponentiate update (Lie–Trotter / circle-dot product) that behaves like a softmax eigenvalue calculation, iteratively homing to the largest eigenvector; diagonal case recovers ordinary Bayes. Proves MAP-style log-likelihood bounds, shows faster convergence when eigensystems differ, and flags physical realizability as open.
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chapters (21)
- 0:00Introduction
- 0:43Machine Learning
- 1:05Bayesian Rule
- 2:26Density Matrices
- 4:01Degenerate Elliptical
- 6:33Conventional and generalized probabilities
- 7:25Elementary events
- 8:20Graphical models
- 8:48Covariance matrices
- 10:55Gleason theorem
- 11:35Orthogonality
- 12:31Dot Products
- 13:58Measurements
- 15:12Normal Base Rule
- 15:34Bayes Rule
- 31:20Prior Data
- 31:43Relative Entropy
- 33:03Base Rule
- 33:20Inertia
- 37:31Calculus
- 45:58Quantum Zeno Effect
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