# How does measurement-affected spin of an entangled particle not communicate information ftl?

Am I not understanding this video correctly: https://www.youtube.com/watch?v=tafGL02EUOA&t=5m20s

Since up/down or left/right orientation of the particle depends on the physicist's choice at moment of measurement, won't that vertical/horizontal orientation be seen in the other entangled particle? Can't you specify ahead of time what a vertical orientation means and what a horizontal orientation means?

How does measurement-affected spin of an entangled particle not communicate information ftl?

(ftl = faster-than-light)

We can choose the axis along which to measure a particle's spin, but we cannot choose which of the possible outcomes will be obtained. The linked video is describing a special entangled state with this property: If the spins of both particles are measured along the same axis, then the outcomes will be opposite. For example, if we measure both spins along the vertical axis, the combination of outcomes may be either of these:

• the first particle has spin-up and the second particle has spin-down,

• the first particle has spin-down and the second particle has spin-up.

The outcomes are also opposite if some other axis is used instead. This correlation is predictable. However, for the type of entangled state discussed in the video, we cannot predict which of the two possible outcomes will be obtained for either particle individually, and this is why the phenomenon cannot be used for faster-than-light communication.

When a sequence of many such entangled pairs is generated, the sequence of outcomes for any one particle individually is completely unpredictable, no matter what sequence of axes we measure. (There are other types of state in which the degree of unpredictability is reduced, but here I'm talking about the case described in the video.) What is predictable is the fact that whenever we measure both particle's spins along the same axis, the outcomes are opposite. But this does not enable faster-than-light communication, because neither Alice nor Bob can control which outcome is obtained when that party's spin is measured. They cannot encode any message in the sequence of outcomes, simply because they cannot control the outcomes. Therefore, this phenomenon cannot be used for faster-than-light communication.

This phenomenon can be used for something else, though, namely something called Quantum Key Distribution (QKD). This is a relatively new technology that can be used to distribute a secret "key" that two parties can later use to encrypt/decrypt a secret message — which is transmitted at ordinary (not faster-than-light) speeds.

Here's how this type of QKD works: Both partices, Alice and Bob, agree in advance on two different axes along which they might choose to measure the spin of a particle. This information is public. While Alice and Bob are far away from each other, a sequence of entangled particle-pairs is generated (the same type of entangled pair that the linked video describes). For each pair, one of the particles goes to Alice and the other goes to Bob. Each time Alice receives a particle, she randomly chooses which of the two axes to measure, and she records the sequence of outcomes like this: $$\begin{matrix} \text{Axis:} & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 2 & 1 \\ \text{Outcome:} & +1 & -1 & -1 & -1 & +1 & -1 & -1 & +1 & -1 & +1 \end{matrix}$$ Bob also randomly chooses which of the two axes to measure, and he records the sequence of outcomes like this: $$\begin{matrix} \text{Axis:} & 2 & 1 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 \\ \text{Outcome:} & -1 & +1 & -1 & +1 & -1 & +1 & +1 & +1 & +1 & -1 \end{matrix}$$ Bob's choices of which axes to measure happen to be the same as Alices in some cases and happen to be different in other cases. In those cases where they happened to use the same axis, their outcomes are opposite. Alice and Bob both keep their outcome-sequences secret, but one of them, say Alice, publically announces the sequence of axes that she used in the measurements. Bob compares Alice's sequence of axes to his own, and then publically announces the list of cases in which they both used the same axes. Now they both know that Alice's table looks like this: $$\begin{matrix} \text{Axis:} & X & 1 & X & 1 & 2 & X & 2 & X & X & 1 \\ \text{Outcome:} & X & -1 & X & -1 & +1 & X & -1 & X & X & +1 \end{matrix}$$ where $$X$$ indicates information that Bob either doesn't know or doesn't need to know. Most importantly, they now both have a shared sequence of (opposite) outcomes, so either one of them can use this sequence (if it's long enough) to encode a message, and then the other one can use the sequence to decode the message.

The key remains secret because even though Alice publically announced her sequence of axis-choices, the corresponding sequence of outcomes remains unpredictable.

Again, this phenomenon cannot be used for faster-than-light communication. At no point does either party (Alice or Bob) ever learn anything from the other party more quickly than the speed of light would allow. What they do gain is secrecy.

• " They cannot encode any message in the sequence of outcomes, simply because they cannot control the outcomes." But they can control whether the measurements are vertical (up/down), or horizontal (left/right). If Bob decides to measure vertically, then won't Alice measure the opposite vertical spin and not a horizontal spin? If Bob chooses to measure vertical, and observes a down spin, then Alice will not see down, left, or right. If Bob chooses to measure horizontal, and observes right spin, then Alice will not see up, down, or right. They can control the possible outcomes. Right? – EternalPropagation Nov 13 '18 at 17:50
• @EternalPropagation For the type of particle being used here, the only possible outcomes of a measurement along the vertical axis are up and down (not left or right), and the only possible outcomes of a measurement along the left-right axis are left and right (not up or down). If Alice measures along the left-right axis, then she will get either left or right, not up or down, even if Bob measured along the vertical axis and got either up or down. If Alice's measurement axis is orthogonal to Bob's, then their results will be completely uncorrelated (for the type of state used here). – Dan Yand Nov 13 '18 at 22:57
• So it's possible to measure an up spin in one particle and a left spin in the other? – EternalPropagation Nov 14 '18 at 0:05
• @EternalPropagation Yes, that is correct. – Dan Yand Nov 14 '18 at 0:59
• Then what happens if you bring an up spin and a left spin together? Can they recohere? – EternalPropagation Nov 15 '18 at 0:04