Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Generalized Probability Calculus for Density Matrices   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 density matrix is
restricted to be diagonal.
  We develop a probability calculus based on these more general distributions
that includes definitions of joints, conditionals and formulas that relate
these, including analogs of the Theorem of Total Probability and various Bayes
rules for the calculation of posterior density matrices. The resulting calculus
parallels the familiar "conventional" probability calculus and always retains
the latter as a special case when all matrices are diagonal. We motivate both
the conventional and the generalized Bayes rule with a minimum relative entropy
principle, where the Kullbach-Leibler version gives the conventional Bayes rule
and Umegaki's quantum relative entropy the new Bayes rule for density matrices.
  Whereas the conventional Bayesian methods maintain uncertainty about which
model has the highest data likelihood, the generalization maintains uncertainty
about which unit direction has the largest variance. Surprisingly the bounds
also generalize: as in the conventional setting we upper bound the negative log
likelihood of the data by the negative log likelihood of the MAP estimator.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph