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.

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