Bell measurement of distant particles

[Heidi]

Hi Pf
I am looking at the figure in wiki about quantum teleportation.
https://en.wikipedia.org/wiki/File:Quantum_teleportation_diagram.PNG
A wants to send a qubit to B . She receives another qubit from a spdc.
so she has to make a Bell measurement on them. Has these qbits to be close in space and time to do that?

 

[DrChinese]

Hi Pf
I am looking at the figure in wiki about quantum teleportation.
https://en.wikipedia.org/wiki/File:Quantum_teleportation_diagram.PNG
A wants to send a qubit to B . She receives another qubit from a spdc.
so she has to make a Bell measurement on them. Has these qbits to be close in space and time to do that?

In the diagram you reference: No, A and B can be as far apart as you like. However, a classical signal must go from A to B so that a determination can be made as to the proper operation(s) to execute so that the exiting photon is a proper clone of the original.

 

[Heidi]

I am afraid i misspoke my question. it is only about the two photons that Alice has. at t she receives a photon from the spdc but what about the other photon (the ϕ)
What if she receives it at a time t0 before or after t?
can a bell measurement be done with distant qubits at t?

 

[DrChinese]

I am afraid i misspoke my question. it is only about the two photons that Alice has. at t she receives a photon from the spdc but what about the other photon (the ϕ)
What if she receives it at a time t0 before or after t?
can a bell measurement be done with distant qubits at t?

No. To do a Bell State Measurement (BSM), the 2 particles must arrive at nearly the same time - so as to be indistinguishable. They are routed into a PBS apparatus together, and then you look for a pair of detections at the output ports.

As a general rule, PDC pairs cannot be produced upon demand. So in many (most) cases, the photons being subjected to the BSM will not arrive together within a small enough time window.