A Is entanglement also for time-like intervals?

[Heidi]

Hi Pfs,
I read that entanglement is related to a set of paticles that interacted in the past.
When Bob and Alice share two entangled particles there is a space like interval between their
measurements. I wonder if there is also time like entanglements.
suppose that Bob receive his particle a t = 0 and get a up in a given direction.
At t = 0 Alice receive her particle but do not measure the spin in the same direction. She only keeps it near her and waits. Bon measurement was at (-x,0) Alice will measure it at (x,T) whe the interval will be time like. Will she get the same result?
Another thing: when she repeat another time the same measuement is it still a kind of entanglement between two évents of the same particle?

 

[DrChinese]

I read that entanglement is related to a set of particles that interacted in the past.
When Bob and Alice share two entangled particles there is a space like interval between their
measurements. I wonder if there is also time like entanglements.

suppose that Bob receive his particle a t = 0 and get a up in a given direction.
At t = 0 Alice receive her particle but do not measure the spin in the same direction. She only keeps it near her and waits. Bob's measurement was at (-x,0) Alice will measure it at (x,T) when the interval will be time like. Will she get the same result?

There is time-like entanglement, in fact essentially all measurements of the type you describe have a time interval of some type between them. There are several rules to consider:

1. Measuring 2 entangled particles perfectly simultaneously is impossible. One measurement precedes the other by some delta (however small) no matter what you do. Some people would add that special relativity prevents that as well.

2. The order of measurement - Alice first or Bob first - makes no observable difference. The quantum prediction does not change.

3. And in fact, you can even measure one entangled particle before the second entangled particle is created. As strange as it might seem, this can be done using entanglement swapping. See this reference:

https://arxiv.org/abs/1209.4191
"The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime."

 

[PeterDonis]

When Bob and Alice share two entangled particles there is a space like interval between their
measurements.

Not necessarily. In fact QM predicts that the correlations between their measurements are the same regardless of whether the spacetime interval between the measurements is spacelike, timelike, or null.

 

[Heidi]

Another thing: when she repeats another time the same measuement is it still a kind of entanglement between two évents of the same particle?

If we can talk not only about entangled particles but also about entangled measurements result, can we see that repeated measurements always give the same result come from a kind of entanglement ? it would not require a trajectory of the state between the measurements.