Quantum entanglement does not work like that

Whenever the topic of quantum entanglement -- which Einstein decried as "spooky action at a distance" -- comes up in online conversation, somebody will always ask whether this phenomenon can be used for instantaneous communication. And this is a very reasonable question because although the answer is definitively No, it's far from intuitively obvious why this is so, not least because it depends on details of quantum behavior usually omitted from non-technical explanations -- details that are critical to understanding the phenomenon.

I originally wrote the explanation below in response to a post on Gizmodo. Several people said it was helpful, so I decided to preserve it online for when the question inevitably comes up again.

The Very, Very Short Version

Entanglement allows you to infer what result somebody else's experiment will get; but it doesn't allow you to influence what result they will get.

The long version:

First, entangle your electrons

Suppose you “entangle” two electrons (there are lots of ways to do this; we'll take it as given). What this means is that they are paired in such a way that certain of their properties are reflections of each other. (In technical language we would say they have a "shared state".) In particular, we are interested in the so-called "spin". So you send me one electron and keep the other. Now you measure yours to see if it's spin is pointed up or down; if you find yours is up, you’ll know that if I do the same experiment, mine is pointed down; and vice versa. (The entangled electrons are always opposite, like two sides of a coin). 

Importantly, you won’t know whether you’ll get up or down until you do the experiment -- it’s a coin toss. The only way to tell which is the Up electron and which is the Down, by definition, is to do the measurement. 

Anyway: so far, so normal. Up to this point, it's really no more surprising than if you had split a coin down the middle and sent one half to me. It's no surprise that if you kept the heads side, I got the tails side.

But note the really important part here: I can't use this to send you a signal. The typical misunderstanding at this point is to think that since the electrons are always opposite, if I somehow force my electron into the Up position before measuring, yours will instantaneously be in the Down position, and from there with enough entangled electrons I can easily construct a binary code. And the simple fact is, entanglement does not work like that. Although the electrons are opposite to begin with, anything I do to change the state of my electron does not change the state of yours; instead it just breaks the entanglement. I can no more flip your electron by flipping mine than I can turn your half of the coin from heads to tails.

Let's get spooky

But now it gets quantum. Unlike a coin, there are lots of ways you can measure spin: in fact you can choose any axis you want to measure it along. You don’t have to measure whether your electron is pointing up or down like this: |. You could measure whether it is pointing left or right, like this --. Or along any in-between axis, like / or \. 

Now here's the critical part: electron spin is quantized. This means that whatever axis you measure spin on, the answer will always be precisely "+1" or "-1" units of spin (using the units that physicists typically choose), regardless of what state you thought the electron was previously in; in other words, either clockwise or counterclockwise. Yes, even if you think your equipment only generates up and down electrons, if you choose to measure it on the left-right axis, its spin will definitely be measured as either one unit of left or right spin. Oh, and of course if I measure mine on the same axis, it is pointing the other way. Or you could measure it on any orientation in between, and if I measure it on the same orientation, I get the opposite.

There is no analogy in the macroscopic world for this behavior that I can think of. If you had, say, a spinning basketball and you measured it's spin as "+1" in the up/down axis, it's spin on the left/right axis would be 0, and its spin in the / or \ directions would be somewhere between 0 and 1. This is a crucial difference between the quantum world and the familiar classical world.

One of the things this tells us is that, unlike basketballs and other classical objects, electrons don't have a definite spin until you measure it (and even then, that spin is only good until you measure it again on a different axis).

It gets worse (or maybe better)

Now, we’re not done. Up to now we've always measured our electrons on the same axis. It gets even spookier if you and I choose to measure our electrons along different orientations. 

Suppose you measure on the | axis and, say, get Up; but I choose to measure on the -- axis. Now two things I said above seem to be in conflict: 

• entangled spins are always opposite, so mine must be Down; but 
• if I measure left/right I must get precisely left or right. 

So what happens? Well, in fact I get left or right, and with an equal chance of each. It’s as if my electron was pointing Down after your experiment, and randomly chose which of left or right to flip to when I measured it.

Notice, by the way, that when I do my measurement, nothing now happens to your electron. If you were to subsequently measure your electron on the -- axis, your result would be completely random. The moment you measured your electron the first time, the entanglement was over. So no amount of cleverness with repeated measurements will let me send a signal either.

The really hard part

Now I do something even more interesting: instead of measuring --, I set my equipment at an angle to yours, lets say at /. If we think of a clock face with Up/Down at 12 o’clock / 6 o’clock, I set mine at 1 o’clock / 7 o’clock. Now what happens? 

What I find is that when your result is Up (12), I’ll get 7 most of the time and 1 some of the time (the exact proportions can be predicted, and have been demonstrated experimentally literally billions of times). And if your result was Down (6), I get the opposite results; mostly 1, some 7. Somehow, my electron “knows” what axis you measured along and what result you got -- even though the orientation was not fixed at the beginning before the electrons separated. In fact, even the orientations of our measurements can be chosen long after the electrons have separated, yet the entanglement still occurs. 

So maybe there's something here that can be used to communicate? Maybe you can send a signal with the way you choose the axis you measure on, since that influences the distribution of my measurements on a different axis? 

Unfortunately, no. And the reason is this:

Remember that when you measure on your end, you always get a random result, either up or down. You can’t force your electron to Up, and thereby influence my distribution; you can only discover whether it is Up or Down (and then infer what I am seeing). You can choose the axis you measure on, but not the outcome you get. (You can't even "separate out" the Up electrons from the Down: the only way to know which is which is to measure them, which destroys the entanglement.) And since you are getting 12 or 6 at random, to me it looks like I'm getting 7 or 1 at random too.

One last throw of the dice?

So perhaps there is one last loophole. If being entangled affects the measurements I get, maybe there is some way I can tell whether our electrons are still entangled? Since entanglement breaking is also instantaneous, maybe that in itself can be used to send a message? But no. Even while our electrons are still entangled, your stream of results looks completely random to you. Similarly on the other end, whatever I measure looks completely random to me: 1 or 7, 7 or 1, with no pattern. It’s only when we bring our results together that we see that whenever you got 12 I was more likely to get 7, and whenever you got 6 I was more likely to get 1, thereby proving that our electrons were entangled.

This is what physicists mean when they say our results are correlated, and the degree of correlation (as mentioned above) is precisely predictable, and has been tested in the lab. But it's only by bringing our results together that we see the correlation -- in isolation, each of us appears to get a random series of results. And bringing our results together to compare requires conventional slower than light communication.

(By the way, this is the basis of quantum cryptography, but that's a long story for another time.)

So in summary...

A lot of the confusion here comes from non-technical explanations being loose in their language when they say that one electron "influences" the other. This is true in the sense explained above -- the result I measure is linked at a distance (yes OK, Albert, "spookily") to the result you measure. But it's not true in the sense that you could change your electron and instantaneously cause a change in my electron. Any change you make to your electron in an attempt to change mine simply breaks the entanglement, and our results are no longer connected in any way.