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 where for Alice and for Bob. denotes the axis along which Alice measures the spin and the one for Bob. (For the CHSH inequality, one has and 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.
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.
Here is a summary in tabular form of these 2 leading interpretations of quantum mechanics
|Variables||Preskill’s model||Pooch model|
|(Persons) Alice, Bob, Eve||(Dogs) Alice, Bob, Mimi|
|doors 1,2,3||spectacles A, B, C|
|green, red balls||cat, squirrel|
And here is monogamy for dogs: