An idea about using quantum entanglement for "quantum communication at a distance"

This is an idea that originated on the afternoon of March 30, 2023.

Every time I read popular science articles about quantum mechanics, when it comes to the non-locality of quantum entanglement, it is always mentioned that this non-locality cannot be used for effective information transmission, otherwise it would violate the theory of special relativity.

Although a single measurement itself cannot transmit information non-locally, we can use certain rules to transmit information.

For easier understanding, let's imagine the following scenario together:

  1. We define the spin state of a particle as signal 0 when it is up and signal 1 when it is down.
  2. We define the effective signal we transmit as the last result of a continuous observation of the same kind of particle. Once we obtain an effective observation signal, we switch to another kind of particle for observation in order to differentiate between preceding and subsequent signals.
  3. We prepare a sufficient amount of two kinds of particles, such as electrons and photons. Let the electrons become entangled and split into two parts. Then let the photons become entangled and split into two parts.
  4. Now we board a spaceship and leave the Earth, taking with us one entangled electron and one entangled photon.
  5. When we need to send a message to Earth, we start observing the entangled particles in our hands. For example, if we want to send the binary signal "111" to Earth, we start with observing the photons. Since the observed results are unpredictable, we cannot expect every signal to be transmitted to Earth through a single observation. Now we take out one of the entangled photons in our hands and start observing it. The observation will cause the collapse of its spin superposition state, and the result of the collapse is unpredictable. We continuously observe a series of photons until a down-spin photon appears (it can be obtained in the first observation, or it may appear in the nth observation, but if it appears in the nth observation, then all previous observation results are abandoned, and only the signal of the last down-spin photon is considered valid). At this point, we consider that we have transmitted our first signal to Earth. Then we switch to observing the electrons, and continue until a down-spin electron appears. We stop observing the electrons and start observing the photons again. Following the same procedure, when a down-spin photon appears, we stop observing. At this point, on Earth, the entangled particles with the series of photons and electrons we observed will simultaneously collapse and obtain the signal "up-up-up". The staff on Earth can then know that the signal sent from the spaceship is "down-down-down", and they have obtained the information "111" that we want to transmit.
  6. To avoid an unlucky situation where someone cannot obtain the required observation result, we can further specify that when there are 30 consecutive identical signals, this signal is converted to the opposite signal. And we start observing another kind of particle to transmit the next signal. For example, let's consider the signal "111" again. When we observe the photons for the first time, if we observe "up-spin" continuously for 30 times and do not get the "down-spin" signal we need, we stop observing the photons and start observing the electrons, and convert the previous consecutive 30 "up-spin" signals into 1 "down-spin" signal. In the end, we can always obtain the signal "111".

Doesn't this complete the non-local transmission of information?

Another simpler solution can be like this:

  1. We still take enough photons and electrons with us. At this point, all the photons and electrons in our hands are in a quantum superposition state, and their spin states are unknown.
  2. We define signal 0 when measuring photons and signal 1 when measuring electrons.
  3. When we need to transmit information to Earth, we don't care about the spin state of the particles we observe. Instead, we focus on which kind of particle we observe. This time, we transmit the signal "1011" to Earth. We observe an electron for the first time, causing its superposition state to collapse, and at the same time, the entangled electron on Earth also collapses. We know that the first signal we obtained is "electron". Then we observe a photon, and then continue to observe two electrons. We have sent the signal "1011" back to Earth.

I don't know if this can achieve non-local transmission of information. I seek guidance from experts.

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