# Quantum Bayesian Networks

## August 20, 2012

### The Secret Romance Between Information Theory Inequalities and Networks

Filed under: Uncategorized — rrtucci @ 8:30 pm

Check out my new paper:

“Some Quantum Information Inequalities from a Quantum Bayesian Networks Perspective”, by Robert R. Tucci, arXiv:1208.1503 (abstract here)

There are

the inequalities of SIT (Shannon Information Theory) and of Thermodynamics (e.g. that minor inequality $\delta S \geq 0$)

and then there are

networks,

and never the twain shall meet?

Of course not.

In classical SIT, a well known inequality is the so called Data Processing Inequality which says that any Markov chain

$\underline{c}\leftarrow\underline{b}\leftarrow\underline{a}$

satisfies

$H(\underline{c}:\underline{a})\leq H(\underline{b}:\underline{a})$

In other words, the correlation between $\underline{a}$ and $\underline{b}$ is larger than the correlation between $\underline{a}$ and node $\underline{c}$, which is more distant from $\underline{a}$ than node $\underline{b}$.

But a Markov Chain is just a super simple network. Why stop there? Why not consider more complicated networks? And why limit yourself to classical SIT. Why not quantum SIT too? See my new paper for a pedagogical introduction to the secret romance between SIT and Bayesian networks, a romance which goes on in both classical and quantum physics.