When Spooky Action Comes in Threes

A fan wrote me today and asked about a passage from Superposition, in which a character explains quantum entanglement using coins as an analogy.  He asked: What if there were three coins instead of two?  I enjoyed writing up the answer, so I thought I’d post a portion of it here:

In the analogy, I gave my “particles” a binary attribute (heads or tails) to show their relationship in an easy, intuitive way.  In real life, entangled particles are produced such that they each share a part of some initial value.  For instance, one particle decays into two smaller particles, and the attributes of the two smaller particles have to add up to the attribute of the original one.  You don’t know what the values are, but once you know one value, you know the other one for sure.  So, yes, you can entangle three (or more) particles, though it’s harder to do.  Which just means that there will be some value (or set of values) that connect them, because of how they were made.
So to relate it back to the coins, if you had two impressions of side A of the coin, and one impression of side B, and you looked at the B-side impression and saw heads, then you would know that both of the other impressions were tails.  If you looked at one of the side-A impressions and saw heads, then you would know that the other side-A impression was heads, and the side-B impression was tails.  In all cases, the particles are entangled, which means that the values are related, such that if you determine one, you know the others.  But because of quantum uncertainty, the values aren’t actually determined until you measure it.  (Which is the bit demonstrated by the double slit experiment.)
It may seem as if this would allow for faster-than-light communication, since the entangled particles clearly pass information faster than the speed of light.  (This is the concept behind the ansible, as referenced in novels by Ursula K. LeGuin and Orson Scott Card.)  But it actually can’t work that way.  There’s no way to control the values, so there’s no way for a human to pass information that way.  It could, however, be a fantastic one-time pad for encryption purposes.  If I have a set of entangled particles, and you have the matching set, then I can use the first N values of mine to encrypt a message and send it to you.  When you receive the message, you use the first N values of yours to decrypt the message, and voila.  Encryption no one can break, with a key that no one else could possibly have a copy of, since the values weren’t even determined until I encoded my message.  As long as no one has stolen your cache of entangled particles, our messages are safe.
All this stuff is what makes quantum mechanics fun!  And also, crazy and mind-blowing.  Thanks for reading!

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