Transferring information faster than the speed of light

[Reality Researcher]

TL;DR Summary

An idea that I have about communication between two sites faster than the speed of light.

Hi,

I thought of a mechanism that should allow the transfer of information between two sites (between two places) at a speed faster than the speed of light, at least theoretically.

I want to hear what the experts here think about it, because it's quite clear to me that I probably have some mistake since I know that this is supposed to be completely impossible.

So:

From the little knowledge that I have in quantum physics, I remember that it is possible to transfer a random encrypted key to a remote location (for example, to the Andromeda galaxy, which is 2,500,000 light years away from here) in such a way that the receiver at the remote location can know if any third party looked at the key before him (i.e., performed eavesdropping).

The key can be composed, for example, of a group of photons, each of which is entangled with a twin photon that remains on Earth.

So my basic assumption is that it is possible to transfer a key to a remote location, and that whoever receives it will be able to know if a third party looked at the key before him (the one sent to him, or the key that remained on Earth - looking at either of them will immediately cause the photons to collapse to some random state).

So far, so good?

Will the person in Andromeda (who received the key) be able to know if someone looked at it before him?

If so far everything is correct, then what about the following situation:

1. We send 100 separate keys to the person in Andromeda, and in the meantime, he hasn't looked at any of them (but they are already in his possession).

2. Now, let's say we want to send him a message, for example, the number 12345, whose binary value is 11000000111001. We will look on Earth at keys number: 1, 4, 5, 6, 13, 14 which represent the bits with value '1' in the number 12345, and cause them to collapse.

3. An hour later, the person in Andromeda will check the keys in his possession, will see that keys 1, 4, 5, 6, 13, 14 have been eavesdropped on (i.e., someone looked at them before), will convert them to binary code, then to decimal, and will receive the number 12345.

This means that the person in Andromeda received the code we sent him (12345) within an hour - instead of millions of years, which is much faster than the speed of light...

Where is my mistake?

 

[Nugatory]

Will the person in Andromeda (who received the key) be able to know if someone looked at it before him?

No, and that’s why your idea will not work. There are already many many older threads explaining this (and you can also Google for the “quantum non-communication theorem”).

 

[Reality Researcher]

No, and that’s why your idea will not work. There are already many many older threads explaining this (and you can also Google for the “quantum non-communication theorem”).

So what is that mechanism that allow the persons sending the key knows if someone looked at it?

There is such mechanism, isn't that right?

(At least in theory)

 

[Klystron]

Information in your thought experiments does not "communicate between sites." Presumably, some mechanism exists to transfer the keys from Earth to Andromeda at some plodding velocity.

Consider using Earth and Luna for your experiment. Or Albuquerque to El Paso. Will not help the answer but its closer to home.

 

[Nugatory]

So what is that mechanism that allow the persons sending the key knows if someone looked at it?

There is such mechanism, isn't that right?

(At least in theory)

The effect of the tampering is that the two sides don’t measure the same key, so can’t decrypt the messages sent using ordinary non-FTL methods - they get gibberish. But until that happens they have no way of knowing that the received key is not the same as the sent key.

 

[Nugatory]

Information in your thought experiments does not "communicate between sites." Presumably, some mechanism exists to transfer the keys from Earth to Andromeda at some plodding velocity.

Quantum cryptography works exactly the other way - the whole point of the entangled particles exercise is to distribute the keys instantaneously and securely.

The keys are exchanged faster than light, but no information transfer happens until someone uses the shared key to encrypt a message that then has to be sent by normal means and the decrypted by the recipient.

 

[Klystron]

Quantum cryptography works exactly the other way - the whole point of the entangled particles exercise is to distribute the keys instantaneously and securely.

The keys are exchanged faster than light, but no information transfer happens until someone uses the shared key to encrypt a message that then has to be sent by normal means and the decrypted by the recipient.

Yes, I should have stipulated "physical keys", not the encryption also labeled key.

 

[Reality Researcher]

The effect of the tampering is that the two sides don’t measure the same key, so can’t decrypt the messages sent using ordinary non-FTL methods - they get gibberish. But until that happens they have no way of knowing that the received key is not the same as the sent key.

Very good answer, thanks!

So that was the main mistake in my theoretical experiment...

They will know that someone looked at the keys ONLY after the person in Andromeda get the first message and see that it's gibberish...

 

[Reality Researcher]

The effect of the tampering is that the two sides don’t measure the same key, so can’t decrypt the messages sent using ordinary non-FTL methods - they get gibberish. But until that happens they have no way of knowing that the received key is not the same as the sent key.

I thought about that again, and it's still not clear.

If the key's photons on Earth are entangled with key's photons on Andromeda, then why does it matter if:

1. The man on earth looked at them first.

2. The man in Andromeda looked at them first.

3. A third party person preceded them and looked at the key first.

Shouldn't the result be exactly the same in each of the three situations? Meaning, the photons of the key on Earth and the photons of the key in Andromeda will collapse one into the opposite state of the other, in a synchronized way?

What am I missing?

 

[DrChinese]

I thought about that again, and it's still not clear.

If the key's photons on Earth are entangled with key's photons on Andromeda, then why does it matter if:

1. The man on earth looked at them first.

2. The man in Andromeda looked at them first.

3. A third party person preceded them and looked at the key first.

Shouldn't the result be exactly the same in each of the three situations? Meaning, the photons of the key on Earth and the photons of the key in Andromeda will collapse one into the opposite state of the other, in a synchronized way?

What am I missing?

Items 1 and 2 are correct. There is no observable difference.

 

[PeterDonis]

What am I missing?

It's not a question of when anyone looks at the key. It's a question of when the message recipient knows that the key either works or doesn't work. Just looking at the key doesn't tell you that. As has already been said, the message recipient can't know whether the key they looked at actually works until they receive an encrypted message by normal light speed (or slower) transmission and either can or can't decrypt it.

 

[Nugatory]

What am I missing?

The protocol works in such a way that any measurement of either particle made by an intruder will change the state of the entangled pair in such a way that Andromeda-guy is no longer guaranteed to get a result that correlates to Earth-guy’s. Thus Andromeda-guy’s key won’t match Earth-guy’s if there is a third party involved.

 

[Reality Researcher]

The protocol works in such a way that any measurement of either particle made by an intruder will change the state of the entangled pair in such a way that Andromeda-guy is no longer guaranteed to get a result that correlates to Earth-guy’s. Thus Andromeda-guy’s key won’t match Earth-guy’s if there is a third party involved.

I understand that this is the claim, but what is the explanation for that?

Why would the key in Andromeda stay sync with the key on Earth when the man in Andromeda looks at it, but go out of sync when a third party looks at it?

How does the key in Andromeda "knows" if the person looking at it is the man in Andromeda that should get the key, or a foreign intruder?

Why there is a different between these two situations?

That's what I don't understand.

 

[Reality Researcher]

Items 1 and 2 are correct. There is no observable difference.

And what about item 3 ?

Why there is a difference?

 

[Reality Researcher]

It's not a question of when anyone looks at the key. It's a question of when the message recipient knows that the key either works or doesn't work. Just looking at the key doesn't tell you that. As has already been said, the message recipient can't know whether the key they looked at actually works until they receive an encrypted message by normal light speed (or slower) transmission and either can or can't decrypt it.

I understood that, my question was why is there a difference between a situation where the man in Andromeda watches the key (and then it stays in sync with the key that remains on Earth) and a situation where a third party watches the key, then it goes out of sync.

Why there is a difference between these 2 situations?

 

[DrClaude]

I understood that, my question was why is there a difference between a situation where the man in Andromeda watches the key (and then it stays in sync with the key that remains on Earth) and a situation where a third party watches the key, then it goes out of sync.

Why there is a difference between these 2 situations?

Because Andromeda will not be looking at the original photon that was entangled with the one on Earth. As soon as the third party measures the state, the entanglement is broken. The third party can only send to Andromeda a photon that is a copy of what they measured, but it is not entangled with the Earth photon, so the "sync" is broken.

 

[DrChinese]

And what about item 3 ?

Why there is a difference?

The person intercepting (say Chris) needs to send on an exact copy of the intercepted photon stream to the person on Andromeda (say Bob). Otherwise Bob will end up with a bunch of gibberish, just the same as if unentangled particles were sent originally.

The photon stream Chris receives is entangled. But it is not possible to copy - i.e. clone - an entangled particle. There's this thing called the "No Cloning Theorem". Yes, Chris can send entangled photons to Bob. But they won't be entangled with Alice's on Earth.

Note what DrClaude says is correct too. If Chris sends a copy of when he measures to Bob, again Bob's photons are no longer entangled with Alice's.

 

[Nugatory]

I understand that this is the claim, but what is the explanation for that?

First, some background.
For definiteness, let’s say say that our entangled particles are electrons and we’re measuring the direction of their spin axis (this is wildly impractical - a real design would use photons and polarizations - but it’s easier to describe and the principle is the same).

An entangled pair is a single quantum system with a wave function that is a superposition. Any measurement causes the superposition to collapse and breaks the entanglement so that afterwards the particles can evolve independently. Say someone measures one of the particles on the vertical axis: That measurement will cause the state of the entangled pair to collapse (with equal probability) to either "Earth particle up, Andromeda particle up" or "Earth particle down, Andromeda particle down". However, if instead they measure on the horizontal axis, the collapse will be to either ""Earth particle left, Andromeda particle left" or "Earth particle right, Andromeda particle right".
A horizontal measurement on a particle that has collapsed to either vertical state will yield "left" or "right" randomly, while a horizontal measurement on a particle that has collapsed to the horizontal "left" or "right" states will yield that as the result with 100% certainty. Likewise, vertical measurements on a particle that has collapsed to one of the horizontal states will yield "up" or "down" randomly, while a horizontal measurement will give the expected "left" or "right" result with 100% certainty.

With that background we can describe the protocol. We have a whole bunch of entangled pairs shared between Earth and Andromeda. For each pair, both people independently make a random choice to measure either the vertical or the horizontal spin. Then they use their ordinary boring subluminal classical channel to send the other a plaintext message describing which orientation they chose for each measurement (but not the actual results!). They use the results for the pairs in which they chose the same direction as the encryption key for subsequent secure communication.
Now suppose an intruder is trying to capture the key so as to be able to eavesdrop. No matter what axis the intruder chooses to measure, sometimes our people will choose the same axis (so will use that bit as part of their key) while the intruder will have chosen a different axis. When that happens there is a 50% chance that the earth/andromeda results won't match, leading to different keys at the the two ends. For example, Earth measures on the vertical axis and get "up", therefore expects that if Andromeda measured on the vertical axis they would also get "up"; however the intruder chose to measure on the horizontal axis so the particle that ends up at andromeda is either "left" or "right" and andromeda's measurement has a 50% chance of being "down" and that bit in the exchanged key being wrong.

If we do the math, we will find that on average our intruder will scramble 25% of the bits in the key. With a realistic key length of several hundred bits, this pretty much ensures that the keys at the two end will be different.

Edit to add: There's a convention used in cryptography discussions: The two people trying to communicate securely (your earth and andomeda people) are "Alice" and "Bob", an eavesdropper trying to listen in will be "Eve", and a malicious attacker trying to alter the communicated messages will be "Mallory". This is common enough that if you're going to continue studying the subject you should be comfortable with it, and use it yourself as other people are more likely to understand you.

 

[PeroK]

Because Andromeda will not be looking at the original photon that was entangled with the one on Earth. As soon as the third party measures the state, the entanglement is broken. The third party can only send to Andromeda a photon that is a copy of what they measured, but it is not entangled with the Earth photon, so the "sync" is broken.

Aren't the protocols to identify interception non-trivial? It's not just a simple matter of measuring polarisation?

 

[Nugatory]

Aren't the protocols to identify interception non-trivial? It's not just a simple matter of measuring polarisation?

Your post crossed mine, I think. Yes, the protocol is non-trivial, even my post above has cut some corners. The wikipedia article on "Quantum key exchange" is not great, but it does go into more detail.

 

[PeroK]

Your post crossed mine, I think. Yes, the protocol is non-trivial, even my post above has cut some corners. The wikipedia article on "Quantum key exchange" is not great, but it does go into more detail.

The OP's confusion may be related to this point.

 

[PeterDonis]

Why would the key in Andromeda stay sync with the key on Earth when the man in Andromeda looks at it, but go out of sync when a third party looks at it?

The third party doesn't have a particle that is entangled with the one on Earth. Only the receiver on Andromeda does. So the third party cannot "look at the key" the way the receiver on Andromeda can. The third party can only "look at the key" by doing something that breaks the entanglement. That is the difference.

 

[gentzen]

The third party can only "look at the key" by doing something that breaks the entanglement. That is the difference.

Why this "dubious" answer, after Nugatory and PeroK already clarified what is really going on? (It is a property of the concrete protocol, and the protocol is far from trivial.)

 

[PeterDonis]

Why this "dubious" answer

It's not "dubious" (note that you quoted one particular sentence out of context), it's correct, and stated more briefly than previous posts in case that helps the OP to grasp what is going on.

 

[Reality Researcher]

First, some background.
For definiteness, let’s say say that our entangled particles are electrons and we’re measuring the direction of their spin axis (this is wildly impractical - a real design would use photons and polarizations - but it’s easier to describe and the principle is the same).

An entangled pair is a single quantum system with a wave function that is a superposition. Any measurement causes the superposition to collapse and breaks the entanglement so that afterwards the particles can evolve independently. Say someone measures one of the particles on the vertical axis: That measurement will cause the state of the entangled pair to collapse (with equal probability) to either "Earth particle up, Andromeda particle up" or "Earth particle down, Andromeda particle down". However, if instead they measure on the horizontal axis, the collapse will be to either ""Earth particle left, Andromeda particle left" or "Earth particle right, Andromeda particle right".
A horizontal measurement on a particle that has collapsed to either vertical state will yield "left" or "right" randomly, while a horizontal measurement on a particle that has collapsed to the horizontal "left" or "right" states will yield that as the result with 100% certainty. Likewise, vertical measurements on a particle that has collapsed to one of the horizontal states will yield "up" or "down" randomly, while a horizontal measurement will give the expected "left" or "right" result with 100% certainty.

With that background we can describe the protocol. We have a whole bunch of entangled pairs shared between Earth and Andromeda. For each pair, both people independently make a random choice to measure either the vertical or the horizontal spin. Then they use their ordinary boring subluminal classical channel to send the other a plaintext message describing which orientation they chose for each measurement (but not the actual results!). They use the results for the pairs in which they chose the same direction as the encryption key for subsequent secure communication.
Now suppose an intruder is trying to capture the key so as to be able to eavesdrop. No matter what axis the intruder chooses to measure, sometimes our people will choose the same axis (so will use that bit as part of their key) while the intruder will have chosen a different axis. When that happens there is a 50% chance that the earth/andromeda results won't match, leading to different keys at the the two ends. For example, Earth measures on the vertical axis and get "up", therefore expects that if Andromeda measured on the vertical axis they would also get "up"; however the intruder chose to measure on the horizontal axis so the particle that ends up at andromeda is either "left" or "right" and andromeda's measurement has a 50% chance of being "down" and that bit in the exchanged key being wrong.

If we do the math, we will find that on average our intruder will scramble 25% of the bits in the key. With a realistic key length of several hundred bits, this pretty much ensures that the keys at the two end will be different.

Edit to add: There's a convention used in cryptography discussions: The two people trying to communicate securely (your earth and Andomeda people) are "Alice" and "Bob", an eavesdropper trying to listen in will be "Eve", and a malicious attacker trying to alter the communicated messages will be "Mallory". This is common enough that if you're going to continue studying the subject you should be comfortable with it, and use it yourself as other people are more likely to understand you.

Thanks very much for the explanation, but I see that it's more complicated than what I thought, and it's a little hard for me to follow.

I'll need to read more about the subject before I can ask more questions about it.

Thanks.