Teleportation is something that most of us have heard of at least once, either in movies, TV shows, books, or in academy, like me. Yes, I’m serious. Quantum teleportation is real, though it might not work the way we see it in movies. This blog post gives you a quick overview of quantum teleportation, a way to send one qubit of information from one place to another without any sort of communication. Before I start the blog, I want to make it clear that it might be hard to understand if you don’t know much about quantum computing. If that sounds like you, I recommend reading some of my other blogs to get a better idea of what I’m talking about. Also, keep in mind that quantum teleportation can never go faster than light because it still follows the theory of relativity.
Teleportation :
In traditional terms, teleportation refers to transferring an element from one place to another in a matter of seconds even over very long distances like from one universe to another. While it may seem obvious in movies, it’s not possible in real life… yet. But if it works, there will be equal growth and chaos in the human race. But enough with the fantasy part; let’s look at how it works in technically.
Quantum teleportation :
Quantum teleportation is not as described above. It transfers one qubit of information from one qubit to another without using communication. Want to learn more about qubits? Check out my blog on Qubit. Assume Alice wishes to convey information to Bob, and she doesn’t need to know the quantum state in which she is teleporting. After teleportation even if Bob knows the knowledge, he has to know the classical information in order to measure his qubit to complete the teleportation. Because classical information must be sent, quantum teleportation is not quicker than light (end of myth).
This blog exhibits single qubit teleportation with bell states. Learn more about superposition and entanglement on my blog. The first scientific paper to discuss quantum teleportation was “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels” by C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters in 1993, which was experimentally realized by two research groups led by Sandu Popescu and Anton Zeilinger.
Ok let’s realize the teleportation circuit. We have 3 qubits in total, as shown below, Qubit0 has unknown state and needs to be teleported to qubit2. First, we need to generate entangled state (bell state) using Hadamard and C-NOT gate on qubit1 and qubit2 and then we apply teleportation protocol as shown in below.
That’s it the information has been teleported to qubit2, It’s that simple here. However, it won’t be the same case in multi qubit. Though qubit2 has all the information, it doesn't know how to get the exact information, so we need to measure first two qubits and send their outcomes to qubit2 to apply respective gate to complete the teleportation. Then we can measure to get the teleported information. In below circuit, we measure first qubit.
After the measurement of first two qubits, we will send the outcomes to qubit2. Based on that, qubit2 applies quantum gate to it’s qubit. Let’s understand mathematically now.
Let |ψ⟩ be our unknown state to be teleported and one of bell states |φ+⟩.
|ψ⟩ = a|0⟩ + b|1⟩
|φ+⟩ = 1/√2 |00 + 11⟩
|ψ⟩ = |ψ⟩|φ+⟩
|ψ⟩=1/√2 (a|0⟩|00+11⟩+b|1⟩|00+11⟩)
Now let’s apply a CNOT gate with control as first qubit and second qubit as target.
|ψ⟩=1/√2 (a|0⟩|00+11⟩+b|1⟩|10+01⟩)
Then hadamard on the first qubit results as,
|ψ⟩ = 1/√2 (a|0+1⟩|00+11⟩+b|0−1⟩|10+01⟩)
We can rewrite the above |ψ⟩ as,
|ψ⟩=1/√2 (|00⟩a|0⟩+b|1⟩)+|01⟩(a|1⟩+b|0⟩)+|10⟩(a|0⟩−b|1⟩)+|11⟩(a|1⟩−b|0⟩)
Now we perform the measurement on the first qubit and with respect to the outcome, we will apply respective gate’s on the second qubit. The protocol goes as below in table, where qubit2 is referred as Bob’s qubit.
The circuit goes as follows:
Now, when we measure on desired computational basis on qubit2, we will get the exact teleported information. Since classical information need to be communicated through classical channel, quantum teleportation is not faster than light, and it follows rules of theory of relativity.
The above protocol can be used to teleport any single qubit teleportation, instead of |0 + 1⟩, we can teleport |0⟩,|1⟩ or superposition too.
I hope with this simple blog you may introduced to quantum teleportation, I understand that for some it may be difficult to get it. As I said earlier, give it 2–3 read. I have also provided references to help you understand. Please feel free to reach out to me for any queries or collaborations and do not forget to provide feedback.
Quantum Teleportation
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Thirumalai Manimaran
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