Can Quantum Entanglement Be Used for FTL Communication?

Quantum entanglement can correlate distant measurement results, even when the measurements are made too far apart for a light signal to pass between them during the experiment. That can sound like faster-than-light communication. The key distinction is that a correlation is not a controllable message: Alice cannot choose the result Bob sees.

What counts as communication?

To send a message, Alice must be able to choose between at least two actions that produce distinguishable outcomes for Bob. For example, she might want to encode a 0 or a 1 by choosing a measurement setting. If Bob’s local data look identical in either case, he has no way to read the message before receiving a conventional signal from Alice.

Entanglement does produce correlations that Alice and Bob can confirm after comparing their results. But Bob cannot infer Alice’s measurement choice or outcome from his results alone. This is the content of the no-signalling principle in quantum mechanics.

A worked example: a spin-singlet pair

Suppose Alice and Bob share two spin-$1/2$ particles in the singlet state. If they measure spin along the same axis, their results are always opposite. Represent each result as $+1$ or $-1$.

If Alice measures and obtains $+1$, Bob will obtain $-1$ when he measures along that same axis. But before Alice tells him her result, Bob cannot know whether she obtained $+1$ or $-1$. His result is equally likely to be either one:

$$P(B=+1)=P(B=-1)=\frac{1}{2}.$$

The same is true if Alice chooses a different measurement axis. In the singlet state, if the axes are separated by an angle $\theta$, the joint probability for results $a,b\in\{+1,-1\}$ is

$$P(a,b)=\frac{1}{4}\left(1-ab\cos\theta\right).$$

To find Bob’s probability of a particular result $b$, sum over Alice’s possible results:

$$\begin{aligned} P(B=b) &=P(+1,b)+P(-1,b)\\ &=\frac{1}{4}(1-b\cos\theta)+\frac{1}{4}(1+b\cos\theta)\\ &=\frac{1}{2}. \end{aligned}$$

The angle affects the joint correlations, but it does not affect Bob’s individual statistics. For identical axes, the results are perfectly opposite; for axes at right angles, they are not perfectly correlated. In neither case can Bob read Alice’s choice from his own outcomes.

Why Alice’s choice does not send a signal

The same point can be expressed using density matrices. Bob’s particle by itself is described by the maximally mixed state $I/2$, where $I$ is the identity operator. This state assigns probability $1/2$ to either result for any spin measurement.

A local measurement by Alice changes the state she assigns to the pair when she conditions on her particular result. It does not change Bob’s unconditioned local state. If Alice’s outcomes are not communicated to Bob, he must average over them, and that average remains $I/2$.

More generally, any physical operation Alice performs locally that is not conditioned on sending her outcome leaves Bob’s reduced state unchanged. Quantum theory therefore does not let her make Bob’s data depend on a freely chosen message. A measurement may update predictions about the joint system, but that update alone is not a usable signal traveling to Bob.

What Bell experiments do show

Bell’s theorem rules out a broad class of theories in which measurement outcomes are explained by shared local hidden variables. Experiments violate Bell inequalities, demonstrating that quantum correlations cannot be reproduced by that class of local models.

This does not imply that information is being transmitted faster than light. The observed correlations become visible when Alice and Bob later compare their measurement settings and results. That comparison requires a communication channel, which cannot carry a message faster than light. Quantum mechanics predicts the correlations without providing a way to use them for faster-than-light signalling.

Common mistakes

• Treating a predictable correlation as a message. If Alice knows Bob’s result after learning her own, that does not mean she chose or controlled Bob’s result.
• Confusing a conditional state with Bob’s local data. A state conditioned on Alice’s reported outcome is useful for predicting correlations, but Bob does not have that outcome until it is sent to him.
• Assuming “instantaneous” means “usable for communication.” A distant measurement can be correlated with Alice’s result without giving her control over the result Bob observes.
• Concluding that Bell violations show all influences are local. Bell tests rule out particular local explanations; they do not establish a faster-than-light communication channel.

Thus, entanglement is nonclassical and has important consequences for experiments and quantum technologies, but it does not allow Alice to send Bob a message faster than light.