# Quantum Bayesian Networks

## May 1, 2013

### Pooch Interpretation of Quantum Mechanics and Doggie Q-Spectacles

Filed under: Uncategorized — rrtucci @ 5:58 pm

For more than a decade, John Preskill has been illustrating Bell’s inequality and related concepts with pictures of balls of two colors (red and green) that can be inserted into a box with two doors, door 1 on the top side, and door 2 on the front side. Here is a small sample of his art work:

Personally, I prefer explaining Bell’s inequality using Bayesian networks. It’s clearer that way, at least to me. I’ve been explaining Bell’s inequalities that way ever since I wrote the manual for my software Quantum Fog more than a decade ago. I’ve also explained them that way previously in this blog in the post entitled “Bell’s inequality for the Bayesian statistician“. Here is a sample of my art work from that previous blog post of mine:

John’s fine art work has made me realize that mine is grievously lacking in empathic cues (i.e., it’s pretty dull). If I had to give a public lecture accessible to non-scientists, I would fail miserably, unless…I enhanced the bayesian networks experience by adding some dog pictures. (if you are a quantum complexity theorist, instead of dogs, you might prefer to add some pictures of yourself in various dashing poses.)

As shown by the above figure of a Bayesian network, Bell’s inequality leads us to consider a variable $x_j^{\alpha_1}\in \{0,1\}$ where $j=1$ for Alice and $j=2$ for Bob. $\alpha_1\in \{A,B,C\}$ denotes the axis along which Alice measures the spin and $\alpha_2\in \{A,B,C\}$ the one for Bob. (For the CHSH inequality, one has $\alpha_1\in \{A,B\}$ and $\alpha_2\in \{A',B'\}$ instead.)

The pooch interpretation of quantum mechanics posits that there are three dogs named Alice, Bob and Mimi that have poor eyesight and require spectacles in order to see/measure an atom, which looks to them like a fuzzy glob without their spectacles on, but which looks like either a cat or a squirrel with the spectacles on. Each dog can wear either spectacles A, B or C, but each of those spectacles gives a different ratio of squirrel to cat sightings for the same neighborhood!

(Previous work: Dogs Playing Poker)

The “Preskill’s 2 balls” model can be mapped into the pooch model as follows.

Replace persons Alice, Bob and Eve by spectacle-wearing dogs named Alice, Bob and Mimi.

Alice

Bob

Mimi

Replace doors 1,2,3… by spectacles with lens types labeled A,B,C, etc. A and B might correspond to linearly polarized and circularly polarized.

Replace red and green balls by pictures of a cat and squirrel. These might correspond to the measurement values of 0 or 1 for the state of a qubit.

Squirrel!! Ruff, Ruff

Cat!! Ruff, Ruff

Here is a summary in tabular form of these 2 leading interpretations of quantum mechanics

 Variables Preskill’s model Pooch model $j\in \{1,2, M\}$ (Persons) Alice, Bob, Eve (Dogs) Alice, Bob, Mimi $\alpha\in \{A,B,C\}$ doors 1,2,3 spectacles A, B, C $x_j^\alpha\in\{0,1\}$ green, red balls cat, squirrel

And here is monogamy for dogs: