# If quantum cloning was possible would entanglement enable faster than light communication?

Assume quantum mechanics allowed you to clone particles. How could you use quantum entanglement to communicate faster than the speed of light?

In the 1980s a scientist proposed using quantum cloning to send information between entangled particles faster than light. This led to the discovery that quantum mechanics prohibited quantum cloning.

• Have you looked at this? en.wikipedia.org/wiki/Quantum_cloning . It seems that "Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non-unit (i.e. non-perfect) fidelity. " and the field is active. – anna v Jun 6 '18 at 4:20

Imagine Alice and Bob share a Bell state:

$$|\psi \rangle = |00\rangle +|11\rangle \ .$$

Note that this state looks like this in the $X$ basis:

$$|\psi\rangle = |++\rangle + |--\rangle \ .$$

As you know if Alice measures her qubit in the $Z$ basis, and gets $|0\rangle$ or $|1\rangle$, Bob's qubit will collapse unto the corresponding state as well. On the other hand if she measures it in $X$ basis, Bob's qubit will also collapse to a state in the $X$ basis.

Now, imagine Alice and Bob have moved to opposite ends of the Milky way, and Bob has made a Billion copies of his qubit. Normally, Bob would be unable to distinguish what basis Alice has measured her qubit, but now Bob can measure half of his qubits in the $Z$ basis and the other half in the $X$ basis. The half that agree with each other shows the basis Alice has measured her qubit in. Therefore, assuming cloning arbitrary quantum states was possible, Alice could instantly send a bit of information to Bob on the other end of the universe.

I have devised a way to theoretically send 1 classical bit of information FTL using 400 entangled pairs and 83% fidelity copies. It surpasses 5 sigma.

It’s already somewhat optimized, but I’m sure I can bring down that 400 number. Say Alice wants to send a classical “1”, She measures her half of 400 entangled pairs. Or she can send a classical “0”, simply by doing nothing (or she’s dead).

Just after, Bob makes two imperfect copies of each. Each new copy will have 83.333% fidelity (5/6). If he makes 20 groups of 20 and averages each group, and then takes the average of the averages, he has his 5 sigma answer.

(5/6) x (5/6) = (25/36)

So midway between half is (43/72) or ~0.597222...

If he gets a higher number, Alice sent a 1

If he gets a lower number, Alice sent a 0, or she’s dead, or asleep, or forgot, etc. A secondary “is she sending” channel would solve this.

And of course two additional channels could be used for Bob to send information to Alice. A full duplex scheme would also be able to lower the 400:1 ratio significantly, as well as verification, etc.

A further optimization would be to use median instead of average.

Incidentally this would also allow information to be sent backwards in time using qubits instead of particles such as photons or electrons. Voila! The world’s first time machine! Of course right now T2, or coherence time, is only on the order of ~1 millisecond. But that number goes up by a factor of 1000 every 10 years, akin to Moore’s law. So by 2035 we should be able to send information ~1,000 seconds back in time. Enough time to buy a lottery ticket or evacuate a small building.

Just remember that anything is possible. We used to think that heavier-than-air flight by humans was impossible; sending voice over a wire, etc.

And sending information faster than light or back in time could create some very strange paradoxes or worse. But that’s your problem not mine ;)

Love, Brandon Penzkover

P.S. Before everyone jumps on me about the measurement basis problem, please remember, this is a network protocol. Bob and Alice would have to agree on a lot of things ahead of time, so of course they would choose some arbitrary angle and keep track of it. You could even use a simple gyroscope. That’s not how I would do it, And I agree it’s not a trivial point, it’s just easy to overcome in a variety of ways.

Another issue people might be wondering is what about security. What if Charles (or Chuck, or Eve) wants to listen in on the conversation? I say let them at first at least! Please can we build the thing and worry about that later? Or not even at all. This is about quantum communication not quantum encryption. There are a lot of other people working on that different but related subject.

• It's tempting to believe that this should be true based on the "fidelity" that quantum states can be distringuished (I thought up a similar situation to what you describe once). But it doesn't work. The easiest way to see it doesn't work is to realize that the density matrix is the right way to look at the system. The density operator encodes all measurement statistics and from the density matrix you can determine that no information can be communicated without an exchange of classical light speed communication. The critical problem with your approach is a misunderstanding of what... – wanderingmathematician Oct 16 '18 at 12:52
• fidelity is and how classical information needs to be extracted with measurements. Fidelity does not mean you can just copy a qubit with 5/6 precision without disturbing the first, repeating arbitrarily many times, and finally extract all this information classically. I suggest you take a look at the book by Nielsen and Chuang to get a better idea of how this fails (particularly ch. 2 and the last 1/3 of the book). – wanderingmathematician Oct 16 '18 at 12:55