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I've started learning Quantum Computing from the Qiskit Textbook and was able to easily understand or work out everything until it came to the working of Quantum Teleportation

I can understand the procedure of it, but cannot understand why it works and was unable to work out the math of it. I also couldn't find any source that explained this is in a more simplistic manner.

Here's the procedure that I have copy-pasted from the textbook:

Step 1: Alice and Bob create an entangled pair of qubits and each one of them holds on to one of the two qubits in the pair.

The pair they create is a special pair called a Bell pair. In quantum circuit language, the way to create a Bell pair between two qubits is to first transfer one of them to the Bell basis ( |+⟩ and |−⟩ ) by using a Hadamard gate, and then to apply a CNOT gate onto the other qubit controlled by the one in the Bell basis.

Let's say Alice owns q1 and Bob owns q2 after they part ways.

Step 2: Alice applies a CNOT gate on q1 , controlled by |ψ⟩ (the qubit she is trying to send Bob).

Step 3: Next, Alice applies a Hadamard gate to |ψ⟩ , and applies a measurement to both qubits that she owns - q1 and |ψ⟩ .

Step 4: Then, it's time for a phone call to Bob. She tells Bob the outcome of her two qubit measurement. Depending on what she says, Bob applies some gates to his qubit, q2 . The gates to be applied, based on what Alice says, are as follows :

00 → Do nothing

01 → Apply X gate

10 → Apply Z gate

11 → Apply ZX gate

Note that this transfer of information is classical.

And voila! At the end of this protocol, Alice's qubit has now teleported to Bob.

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  • $\begingroup$ What part of the algorithm you don't understand? Note, in Step 4, you perform an operation based on the measurement outcome. $\endgroup$ – nippon Mar 17 at 7:08
  • $\begingroup$ Apologies for not making it clear enough. I don't understand why we're different gates depending upon the measurement. I understand that is the way to make teleportation work but I cannot see how it's happening. $\endgroup$ – IE Irodov Mar 17 at 7:11
  • $\begingroup$ @Martin Vesely it indeed helps in understanding the maths behind it, yet I'm not sure if I grasp the intuitiveness behind it, an excellent answer on the question btw. $\endgroup$ – IE Irodov Mar 17 at 9:21
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    $\begingroup$ @IEIrodov: Thanks. I am afraid that it is very hard to explain anything in quantum mechanics (and computing) intuitively (with exception to the most simple things). I would recommed to go step by step in circuit implementing the quantum transportation and see how quantum state of entangled qubits change. Maybe it helps. $\endgroup$ – Martin Vesely Mar 17 at 9:42
  • $\begingroup$ this question is too broad as it stands. You should focus on a specific thing you do not understand about the derivation and ask about that $\endgroup$ – glS Mar 18 at 9:45