\nState 2: VV – HH
\nState 3: HV + VH
\nState 4: HV – VH<\/p>\n<\/blockquote>\nNow, that makes perfect sense to a physicist, but my goal is to explain this to 1) non-physicists, 2) without equations, and 3) with minimal hand-waving. And my question is, what’s the best way to describe this.<\/p>\n
It’s easy enough to describe the basic essence of this measurement– basically, you’re asking whether the two photons have the same polarization or opposite polarizations. That’s straightforward enough, and can easily be explained to a layman. The thing that’s hard to explain is why there are four answers, rather than two.<\/p>\n
<\/p>\n
Common sense would say that “Do you have the same polarization?” is a yes-no question, with only two answers. But there are four possible wavefunctions in the Bell basis, in two pairs that differ only by a phase factor. As someone who’s been doing this for a while, I’m familiar enough with this sort of thing that I no longer wonder what that phase factor means.<\/p>\n
Unfortunately, familiarity doesn’t necessarily equal understanding, certainly not at the level of being able to explain it to someone who doesn’t already have some idea of what’s going on. And I’m really not sure how to say anything about this.<\/p>\n
The real meaning of the sign in VV +\/- HH is something like the relative phase between the HH and VV parts of the wavefunction. I’m not sure how to explain that, though– in particular, I’m not sure how to convince anybody that that makes VV+HH and VV-HH distinct states. <\/p>\n
If you’re talking about a single particle, the usual way of vidualizing this sort of thing physically is via the “Bloch sphere,” where you express the state as a vector pointing to a point on the surface of a sphere. In this picture, the two different signs correspond to points on opposite sides of the sphere. I’d rather not get into that, though. And anyway, I don’t think I’ve seen a two-particle version of the Bloch sphere, presumably because it would need to be in four or more dimenstions.<\/p>\n
If you think about it in terms of the polarization of a single particle, and describe it as a vector, (V+H) would be a polarization of 45 degrees up and to the right, and (V-H) would be a polarization of 45 degree up and to the left. But, of course, HV+VH is not the same thing as (V+H)(V+H), so that doesn’t quite work. That might be the best chance at explaining it, though, and as lies-to-children go, it might not be that bad.<\/p>\n
I’d be happy to have a better explanation, though, so if anybody knows of one, leave it in the comments. I’ll be looking through the various quantum books that I have to see if I can find anything…<\/p>\n","protected":false},"excerpt":{"rendered":"
Kind of a technical question, but typing it out might provide some inspiration, or failing that, somebody might have a good suggestion in the comments. Here’s the issue: I’m starting on a chapter about quantum teleportation for the book, and one of the key steps in the teleportation scheme is an entangling measurement of two… Continue reading How to Hand-Wave Quantum Phase?<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[67,7,23],"tags":[],"class_list":["post-2046","post","type-post","status-publish","format-standard","hentry","category-book_writing","category-physics","category-quantum_optics","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/2046","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=2046"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/2046\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=2046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=2046"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=2046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}