How Quantum Randomness Saves Relativity

How Quantum Randomness Saves Relativity

Chad Orzel

...So, if Alice and Bob want to send messages faster than light, Alice just varies the setting of her polarizer, while Bob keeps his set to look for vertical and horizontal. When Alice's photon comes in with a 50/50 chance of passing the polarizer, Bob knows to call that a "0," otherwise he marks it down as a "1." And then they're passing real information back and forth.

Except, that doesn't work either, thanks to quantum randomness. There's no way to get a probability out of a single measurement, after all-- you just get a single click. If you want a probability distribution, you need to do a lot of measurements and use them to infer the probability (by either frequentist or Bayesian means, as you like). But Alice can't just repeat the same setting 100 times for each bit she wants to send, because even if she's sending a "1" by putting her polarization analyzer vertical, Bob will detect roughly 50 of those as vertical and 50 of those as horizontal, exactly as would be the case for a diagonal polarization. Bob ends up with no actual information from Alice.

If you want to use Alice's polarization measurement to send a message to Bob, what you need is to clone Bob's photon-- make a hundred prefect copies of that one photon, measure them all, and get the probability that way. That would let Bob distinguish diagonal from vertical polarization, and extract Alice's message. But relativity is again saved by the mathematics of quantum physics-- in 1982, Bill Wootters (one of my undergrad professors) and Wojciech Zurek proved a "no-cloning theorem", which forbids the exact operation you would need to send information faster than light using entangled photons. The proof is surprisingly simple and powerful-- just a few lines of algebra, see this quantum wiki or a write-up by Wootters and Zurek (pdf)-- and applies to any arbitrary quantum system. If you know in advance what the state of a system is, you can make many copies (this is essentially how a laser works, using stimulated emission to make many identical photons), but an indeterminate state cannot be faithfully duplicated. Any attempt to copy the state of Bob's photon will necessarily introduce random noise that destroys the attempt to determine the polarization.

So, for all Einstein's complaints about the probabilistic nature of quantum physics, it's that very randomness that serves to protect relativity. Which is very good for those of us who like causes to precede effects...

He's also got a video on the HCP (...yeah you know me...):