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Suppose Alice and Bob have entangled particles A and B that are very far apart. Alice uses Particle A to send information through its spin along the x axis, and Bob uses Particle B to receive this information. Particles A and B

To start, Alice measures Particle A's spin perpendicular to the x axis:

Particle A's spin is measured perpendicular to the x axis

and continually measures it along axes that gradually closer to the desired spin state along the x axis. The more measurements taken to get to the desired state, the better, since that reduces the chance of an error occurring at some point.

Once Alice has reached the desired spin state for Particle A, Bob measures the spin of Particle B.

Particle B's spin is measured, allowing Bob to receive the information

The images I've given show Particle A being measured with spin to the right, then being rotated counterclockwise, but it doesn't always have to be like this. It could be measured with spin left or right and rotated clockwise or counterclockwise, depending on whether Alice wants to set it to up or down.

This process is repeated at regular intervals so that Alice and Bob can make measurements at the right time without communicating, and there are other pairs of entangled particles in case some of them do get misaligned.

Ignoring the logistics of actually setting up a system like this, what keeps this from working?

Comments in this answer to another thought experiment said that quantum entanglement doesn't last that long. Is that why this system fails too?

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Once you measure an entangled state, the "entangledness" gets destroyed and they start behaving like regular spin particles. This is one of the biggest impediments in building quantum computers; they rely heavily on entangled states and a stray photon or something can accidentally cause one of the particles in the quantum computer to get measured which thus destroys the quantum state.

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  • $\begingroup$ You can correlate the speed, trajectory, timing or polarization of two particles. Other than that kind of correlation (which can be interfered with) what do you mean by entangled? $\endgroup$ Commented Feb 14, 2022 at 2:35
  • $\begingroup$ That was the exact kind of entanglement I was referring to. If two photons are entangled to have the same polarization, measuring one photon collapses the entire quantum state and both photons would remain in whichever polarization you measured. $\endgroup$
    – Eli Yablon
    Commented Feb 14, 2022 at 2:45
  • $\begingroup$ If you interact with one of the photons you will either absorb it, change its trajectory, it’s polarization or frequency but it will not effect the other photon at all. So of course they will not be correlated any more. You don’t need the word entanglement. $\endgroup$ Commented Feb 14, 2022 at 2:56
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There is a fatal flaw in your reasoning.

You begin by having Alice measure the spin in the horizontal direction. But she cannot force it to go to the right. Maybe it went to the left ! Impossible to predict which way it went.

Now she starts turning it counterclockwise. You assume it turned to point up, but maybe it turned to point down. Then she measures on the vertical axis. She was able to choose which direction it turned, and by what amount . But since she can't choose where it started from, she can't choose which vertical direction it will be measured. Hence no possibility to send a signal to Bob faster than light.

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  • $\begingroup$ It can also be turned clockwise. Which way it's turned depends on the initial measurement and which way Alice wants to turn it. $\endgroup$
    – zucculent
    Commented Feb 14, 2022 at 1:34
  • $\begingroup$ @zucculent if you are talking about the measuring device being a slit then it’s not that accurate. For example a photon polarized at any angle other than perpendicular can pass through any slit. Just because it makes it through, you still don’t necessarily know what angle it was polarized at before it entered the slit. All you know is that it now has a polarization that matches the slit it just passed through. $\endgroup$ Commented Feb 14, 2022 at 5:33
  • $\begingroup$ @zucculent You are again wrong. I understood the original question as a spin 1/2 particle, where orthogonal wavevectors correspond to opposite directions. The wavevector $\sigma_z=+1/2$ is orthogonal to $\sigma_z=-1/2$ and $\sigma_x=1/2$ is a superposition of these two. $\endgroup$
    – Alfred
    Commented Feb 14, 2022 at 6:17
  • $\begingroup$ @zucculent For photons, orthogonal wavevectors correspond to orthogonal oscillations. An "East-West" oscillating photpn has a wavevector orthogonal to an "North-South" oscillating one. Their superposition with equal amplitude, depending on the phase, can be "NE-SW", “NW-SE” or circular polarisation clockwise or counterclockwise. In all four cases, if you cannot predict what "choice" Alice will find when measuring her photon means that she cannot communicate it to Bob. $\endgroup$
    – Alfred
    Commented Feb 14, 2022 at 6:17
  • $\begingroup$ I was talking about a spin 1/2 particle. I wasn't talking about polarized photons. $\endgroup$
    – zucculent
    Commented Feb 14, 2022 at 22:19

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