Question about the Unitary Operation in Teleportation

In summary, the unitary operation in quantum teleportation, performed by Bob, involves transforming his particle to the original state of Alice's qubit. This transformation requires Bob to identify and distinguish the specific particle, which can be challenging in real experimental situations. Bob needs to know in advance which particle is entangled with Alice's, or he needs to receive the classical message from Alice to determine the correct particle. Otherwise, he will have to apply one of the four possible transformations randomly.
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al onestone
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Question about the "Unitary Operation" in Teleportation

How is the unitary operation actually performed in quantum teleportation(by Bob)? I can never seem to find a thorough explanation of this when I look up teleportation in the literature or on the internet. I understand that Bob's particle is in an unentangled state described by a single qubit pure state, but that it has to be transformed(via a unitary operation) to the original state of Alice's qubit. If you look at it in a real experimental picture, Bob not only has to transform the particle, but he has to distinguish the specific particle which requires the transformation. This means identifying one particle in a whole beam(like a needle in a haystack) and then perform the unitary operation exclusively on it. How is this accomplished? Is Bob somehow able to separate the four possible teleported states without having received the classical message from Alice or does he need to wait for the transmission before he even identifies the correct particle?
 
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al onestone said:
How is the unitary operation actually performed in quantum teleportation(by Bob)?
The procedure is explained in the "Formal presentation" section of the Wikipedia article:
https://en.wikipedia.org/wiki/Quantum_teleportation#Formal_presentation
al onestone said:
If you look at it in a real experimental picture, Bob not only has to transform the particle, but he has to distinguish the specific particle which requires the transformation.
Bob should be able to know in advance which is particle that is entangled with one of Alice's particles...

al onestone said:
Is Bob somehow able to separate the four possible teleported states without having received the classical message from Alice or does he need to wait for the transmission before he even identifies the correct particle?
He needs to know what Alice has measured. Otherwise, the best he can do is apply one of the 4 possible transformations randomly and hope he chose correctly. :smile:
 

1. What is a unitary operation in teleportation?

A unitary operation in teleportation is a mathematical operation that is used to transfer the quantum state of one particle to another particle without physically moving the particles. It is based on the principles of quantum entanglement and superposition.

2. How does a unitary operation work in teleportation?

A unitary operation works by manipulating the quantum state of one particle, known as the input or sender qubit, to become entangled with another particle, known as the output or receiver qubit. This entanglement allows the quantum state of the input qubit to be transferred to the output qubit, resulting in the teleportation of information.

3. What are the applications of unitary operations in teleportation?

Unitary operations in teleportation have various applications in quantum computing, cryptography, and communication. They can be used to transfer information between distant quantum computers, create secure communication channels, and enable teleportation-based encryption.

4. Are unitary operations in teleportation reversible?

Yes, unitary operations in teleportation are reversible. This means that the original quantum state of the input qubit can be recovered from the output qubit by performing the reverse unitary operation. This reversibility is a key characteristic of quantum information processing.

5. What are the challenges in implementing unitary operations in teleportation?

One of the main challenges in implementing unitary operations in teleportation is maintaining the delicate quantum state of the particles involved. Any disturbance or noise can cause errors in the teleportation process. Additionally, the resources and technology required for performing unitary operations on a large scale are still being developed.

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