The Real Reasons Quantum Entanglement Doesn’t Allow Faster-Than-Light Communication

Chad Orzel, CONTRIBUTOR
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If Alice does this on her particle, it does not, in fact, affect the state of Bob’s particle in any way– it’s still in an indeterminate state that’s a mix of 0 and 1. It breaks the correlation between the measurement results, though– Alice’s particle is no longer in a superposition, but only in state 1, so when Bob eventually makes a measurement that randomly picks 0 or 1, it doesn’t necessarily match Alice’s measurement, which is guaranteed to be 1.
It should be noted that the “breaking of entanglement” Ethan describes is actually a slightly tricky thing to do, requiring a fairly specific operation to make it work. You will sometimes hear people assert that entanglement is fragile, and that any disturbance of one of the particles will mess things up, but that’s not true. In fact, there are a huge number of things you can do to change the state of one of the two particles without destroying the entangled nature of the system, provided you keep track of what you did to it and adjust your final measurements accordingly. (I have a blog post and an
arxiv preprint discussing this in more detail…) The impossibility of keeping track of all the ways entangled states get shifted is crucial to (the way I think about) the process of “decoherence” that plays a key role in (the way I think about) the “Many-Worlds” interpretation of quantum physics , which is what I was hinting at when I said this gets into some deep stuff, though this post is already running long, so I won’t try to explain here.
Crucially, though, this is not the sort of thing that people talk about doing when they talk about using entanglement for faster-than-light communication. What they want is a measurement procedure that forces a particular outcome . That is, they want Alice to use some woo-woo mystical process to ask her particle “What is your state?” and make it come out to be 1, thus instantaneously forcing Bob’s particle into state 1 as well. If such a procedure existed, you could, in fact, exploit it to send messages (with disastrous consequences for causality); fortunately, God plays dice with the universe , and the results of a quantum measurement are unavoidably random. Which means that while Alice and Bob end up with measurements that are perfectly correlated, no information passes between them. They can only see the correlation when they get back together and compare lists, and they have to do that at or below the speed of light.
It should also be noted that the version of entanglement-based communication Ethan describes is a particularly naive sort that even fringe physicists mostly reject. A more plausible scheme for actually doing this would be to use different measurement bases to send information. That is, rather than “force the state to be 1 to send Bob a 1,” Alice would ask two different questions of her particle. If she wants to send Bob a 1, she would make a measurement asking “Are you in 0 or 1?,” but if she wants to send a 0 she makes a measurement asking “Are you in ‘0+1’ or ‘0-1’?” The latter operation puts Bob’s particle into the corresponding state, which has a 50% chance of returning either 0 or 1 for his measurement. So all Bob has to do is measure that probability distribution for each particle– if it’s either 0 or 1 with 100% probability, he knows Alice is sending a 1, and if it’s 50% of each, she’s sending a 0.
That scheme doesn’t work either, for a more subtle reason. The problem is that you can’t determine a probability distribution from a single measurement of “0” or “1,” so Bob would need to make a lot of copies of the state of his particle in order to distinguish Alice’s message. But there’s a very deep result (that Kaiser’s book claims was directly inspired by these FTL communication schemes) known as the “no-cloning theorem” showing that this is impossible– you can’t make faithful copies of a quantum state unless you already know what it is. There’s no way for Bob to unambiguously determine which measurement Alice made, so you’re back in the scenario where Alice and Bob each have random strings of 1’s and 0’s that only turn out to be perfectly correlated later on, when they get back together and compare.
Quantum randomness saves the day .
So, as I said, the whole business is subtle and complicated. The end result is always the same, though: While it’s one of the weirdest and coolest phenomena in physics, there is no way to use quantum entanglement to send messages faster than the speed of light.
Chad Orzel is a physics professor, pop-science author, and blogger. His latest book is Eureka: Discovering Your Inner Scientist (Basic Books, 2014).