What point is the entanglement lost

• trosten
In summary, Alice and Bob share two entangled pairs of particles, A/C and D/E respectively. Alice performs a measurement on C and D and sends the result to Bob, who then performs local operations on E. This results in the entanglement of A and E, known as "entanglement swapping".
trosten
Soppuse Alice have two particles A and C that are in a partly entangled state
|Y(A,C)>. We also have another person Bob (ofcourse) with whom Alice share a pair of entangled particles D and E in the singlet state.

Now suppose Alice make a measurement on her two particles C and D, she projects their state onto the Bell basis. And send her result to Bob who performs the appropriate local operations on his particle E. That is Alice teleports the state of particle C to Bobs particle E.

Will E be entangled with A ? If not at what point is the entanglement lost between A and C (or E).

I can perhaps clarify what I mean.

To make this simpler I change the scenario a little.

Alice has the particles A anc C in the state.

|A,C> = (1/sqrt(2))(|00>+|11>)

and she has the particle D which is entangled with Bobs particle E in the similar state

|D,E> = (1/sqrt(2))(|00>+|11>)

now Alice brings particle C and D together and project their state onto the Bell basis and telephones her result to Bob. Who performs the appropriate local operations on E.

Now is A entangled with E ?

Yes. This is called "entanglement swapping" and is the basis for proposals for constructing "quantum repeaters" http://www.arxiv.org/abs/quant-ph/9808065.

1. What is entanglement?

Entanglement is a phenomenon in quantum mechanics where two or more particles become connected in such a way that the state of one particle affects the state of the other, regardless of the distance between them.

2. How is entanglement created?

Entanglement can be created through a process called quantum entanglement, where two particles interact and become entangled with each other.

3. How does entanglement get lost?

Entanglement can be lost through various processes, such as decoherence, where the entangled particles interact with their surrounding environment and lose their entangled state.

4. Can entanglement be regained once it is lost?

It is possible for entanglement to be regained, but it is a challenging and complex process. It usually involves isolating the entangled particles from their environment and carefully controlling their interactions.

5. What are the practical applications of entanglement?

Entanglement has many potential applications in areas such as quantum computing, cryptography, and communication. It also plays a crucial role in quantum teleportation, where quantum information can be transferred from one location to another without physically moving the particles.

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