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A Bayesian Probability Calculus for Density Matrices
Published on Feb 25, 20077921 Views
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the den
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Chapter list
A Bayesian Probability Calculus for Density Matrices00:06
Outline00:37
Outline00:47
Density Matrices?01:00
Ellipses01:19
Ellipses01:31
Eigendecomposition01:44
Ellipses01:50
Eigendecomposition02:01
Density Matrices as mixtures of dyads03:00
Eigendecomposition03:16
Density Matrices as mixtures of dyads03:19
Variance04:00
Plotting Variance04:41
Outline05:10
Conventional Probability Theory05:14
Generalized Probabilites over Rn06:01
Conventional Probability Theory06:53
Generalized Probabilites over Rn06:56
Density Matrices Continued07:13
Probability of Events09:04
Gleason’s Theorem09:27
Outline10:29
Conventional Setup10:30
Conventional Bayes Rule11:22
Bayes Rule for Density Matrices12:08
Non-commutative Bayes Rule?14:00
Conventional Rule Special Case14:52
Intersection Properties15:25
Avoiding Logs of Zeros15:45
Derivation of Updates16:55
Conventional Bayes Rule17:07
Minimization of
17:55
Conventional Bayes Again18:28
Bayes Rule for Density Matrices19:18
Bounds ito MAP19:43
D(y|M)?20:56
Joint Distributions21:11
Joint Probability?21:30
Kronecker Product21:50
Joint Probability21:57
More!22:13
Sample Calculus Rules22:20
Outlook23:09
Bayes Rule for Density Matrices23:41
Avoiding Logs of Zeros26:42
Commutative Matrix Product26:58
Behaviour of the Limit for 27:33
Bayes Rule for Density Matrices28:32
Derivation of Updates30:50
Conventional Bayes Rule31:04
Bayes Rule for Density Matrices31:53
Generalized Probabilites over Rn32:50
Conventional Rule Special Case35:44
Bayes Rule for Density Matrices36:22