Recently I came across the following paper
- Decoherent histories of quantum searching, by Wim van Dam, Hieu D. Nguyen, arXiv:1206.1946
I didn’t look at the paper too closely, but it made me learn a bit about a subject I had never studied before: the decoherent histories (or consistent histories) approach to (or interpretation of) quantum mechanics. This approach is due to Griffiths, Gell-Mann, Hartle, Omnes, and others. Here is a review:
- J.J.Halliwell, A Review of the Decoherent Histories Approach to Quantum Mechanics, arXiv:gr-qc/9407040
- The Net Advance of Physics: DECOHERENT HISTORIES (Interpretation of Quantum Mechanics) here
It occurred to me that quantum Bayesian nets (QB nets) can be used to study consistent histories. Here is how. The following are not very deep observations. What did you expect?! this is a trivial blog for serious people.
Let . Consider a QB net with nodes , where for each , the random variable takes on values .
Let and let be its complement. Let .
Suppose and are both elements of . Note that
Define and to be consistent histories if
We could define it differently. For example, we could ask instead that
where for a particular, fiducial state .