As in Holger Felder's Answer, to make an entangled state, all known ewxperimental techniques are local insofar that entangled states must be 'created' by a single interaction: you need to produce a pure quantum state e.g. of two photons with opposite spin in a given direction, so that the pure quantum state is nonfactorisable (i.e. can't be written in the form $\left.\left|\psi_1\otimes \psi_2\right.\right>$, where $\left.\left|\psi_1\right.\right>$ and $\left.\left|\psi_2\right.\right>$ are independent one-photon states).

Even in theory, two spatially separated particles can become entangled, but only by a special communication protocol between the two particles' locations called Entanglement Swapping (see Wiki page "Quantum Teleportation" and the "Entanglement Swapping" section. The entanglement must be "transmitted" from one location to another.

But I think you're asking whether one can tell whether two particles are entangled when they have been entangled elsewhere and travelled to the experimenter's location. There are two important things to heed here:

1. Any entanglement experiment is like this, even if the detection apparatus is only a few centimetres away from where the entangled particles are produced. So you can in theory detect entanglement arising from photon productions in the next galaxy just as well as you can detect entanglement arising from their production in the next room, as long as you can still access the pairs. In practice, you would be unlikely to know which pairs of photons are meant to be entangled if they just dropped in for afternoon tea in your laboratory casually after having made a journey from M87;
2. NO form of entanglement can be confirmed by the observation of only ONE pair of particles. Quantum mechanical experiments are probabilistic in nature, so the only thing you can do is make many measurements and confirm whether or not the correlations between the measured states is statistically significantly higher than the limits laid down by the Bell Inequality for non-entangled particles.

A kind of exception to point 2. is if you measured the state of one photon and confirmed it to have collapsed to, say, left circular polarisation and measured the other also to have collapsed to the same polarisation then you can say that they were, to within your experimental accuracy, not in the entangled state as follows:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,R\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,L\right>\right.\right)$$

So you could conclude, even after one observation, that they probably were not produced in a single interaction producing photons of opposite spin.

But note that this STILL does not rule out entanglement. There is nothing to say that the photons were not in the following nonfactorisable state before the measurement:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,L\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,R\right>\right.\right)$$

even though I don't know of any experimental apparatus that could make such an entangled state.

As in Holger Felder's Answer, to make an entangled state, all known ewxperimental techniques are local insofar that entangled states must be 'created' by a single interaction: you need to produce a pure quantum state e.g. of two photons with opposite spin in a given direction, so that the pure quantum state is nonfactorisable (i.e. can't be written in the form $\left.\left|\psi_1\otimes \psi_2\right.\right>$, where $\left.\left|\psi_1\right.\right>$ and $\left.\left|\psi_2\right.\right>$ are independent one-photon states).

Even in theory, two spatially separated particles can become entangled, but only by a special communication protocol between the two particles' locations called Entanglement Swapping (see Wiki page "Quantum Teleportation" and the "Entanglement Swapping" section. The entanglement must be "transmitted" from one location to another.

But I think you're asking whether one can tell whether two particles are entangled when they have been entangled elsewhere and travelled to the experimenter's location. There are two important things to heed here:

1. Any entanglement experiment is like this, even if the detection apparatus is only a few centimetres away from where the entangled particles are produced. So you can in theory detect entanglement arising from photon productions in the next galaxy just as well as you can detect entanglement arising from their production in the next room, as long as you can still access the pairs. In practice, you would be unlikely to know which pairs of photons are meant to be entangled if they just dropped in for afternoon tea in your laboratory casually after having made a journey from M87;
2. NO form of entanglement can be confirmed by the observation of only ONE pair of particles. Quantum mechanical experiments are probabilistic in nature, so the only thing you can do is make many measurements and confirm whether or not the correlations between the measured states is statistically significantly higher than the limits laid down by the Bell Inequality for non-entangled particles.

A kind of exception to point 2. is if you measured the state of one photon and confirmed it to have collapsed to, say, left circular polarisation and measured the other also to have collapsed to the same polarisation then you can say that they were, to within your experimental accuracy, not in the entangled state as follows:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,R\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,L\right>\right.\right)$$

So you could conclude, even after one observation, that they probably were not produced in a single interaction producing photons of opposite spin.

But note that this STILL does not rule out entanglement. There is nothing to say that the photons were not in the following nonfactorisable state before the measurement:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,L\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,R\right>\right.\right)$$

even though I don't know of any experimental apparatus that could make such an entangled state.

As in Holger Felder's Answer, to make an entangled state, all known ewxperimental techniques are local insofar that entangled states must be 'created' by a single interaction: you need to produce a pure quantum state e.g. of two photons with opposite spin in a given direction, so that the pure quantum state is nonfactorisable (i.e. can't be written in the form $\left.\left|\psi_1\otimes \psi_2\right.\right>$, where $\left.\left|\psi_1\right.\right>$ and $\left.\left|\psi_2\right.\right>$ are independent one-photon states).

Even in theory, two spatially separated particles can become entangled, but only by a special communication protocol between the two particles' locations called Entanglement Swapping (see Wiki page "Entanglement" and the "Entanglement Swapping" section. The entanglement must be "transmitted" from one location to another.

But I think you're asking whether one can tell whether two particles are entangled when they have been entangled elsewhere and travelled to the experimenter's location. There are two important things to heed here:

1. Any entanglement experiment is like this, even if the detection apparatus is only a few centimetres away from where the entangled particles are produced. So you can in theory detect entanglement arising from photon productions in the next galaxy just as well as you can detect entanglement arising from their production in the next room, as long as you can still access the pairs. In practice, you would be unlikely to know which pairs of photons are meant to be entangled if they just dropped in for afternoon tea in your laboratory casually after having made a journey from M87;
2. NO form of entanglement can be confirmed by the observation of only ONE pair of particles. Quantum mechanical experiments are probabilistic in nature, so the only thing you can do is make many measurements and confirm whether or not the correlations between the measured states is statistically significantly higher than the limits laid down by the Bell Inequality for non-entangled particles.

A kind of exception to point 2. is if you measured the state of one photon and confirmed it to have collapsed to, say, left circular polarisation and measured the other also to have collapsed to the same polarisation then you can say that they were, to within your experimental accuracy, not in the entangled state as follows:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,R\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,L\right>\right.\right)$$

So you could conclude, even after one observation, that they probably were not produced in a single interaction producing photons of opposite spin.

But note that this STILL does not rule out entanglement. There is nothing to say that the photons were not in the following nonfactorisable state before the measurement:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,L\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,R\right>\right.\right)$$

even though I don't know of any experimental apparatus that could make such an entangled state.

As in Holger Felder's Answer, to make an entangled state, all known ewxperimental techniques are local insofar that entangled states must be 'created' by a single interaction: you need to produce a pure quantum state e.g. of two photons with opposite spin in a given direction, so that the pure quantum state is nonfactorisable (i.e. can't be written in the form $\left.\left|\psi_1\otimes \psi_2\right.\right>$, where $\left.\left|\psi_1\right.\right>$ and $\left.\left|\psi_2\right.\right>$ are independent one-photon states).

Even in theory, two spatially separated particles can become entangled, but only by a special communication protocol between the two particles' locations called Entanglement Swapping (see Wiki page "Quantum Teleportation" and the "Entanglement Swapping" section. The entanglement must be "transmitted" from one location to another.

But I think you're asking whether one can tell whether two particles are entangled when they have been entangled elsewhere and travelled to the experimenter's location. There are two important things to heed here:

1. Any entanglement experiment is like this, even if the detection apparatus is only a few centimetres away from where the entangled particles are produced. So you can in theory detect entanglement arising from photon productions in the next galaxy just as well as you can detect entanglement arising from their production in the next room, as long as you can still access the pairs. In practice, you would be unlikely to know which pairs of photons are meant to be entangled if they just dropped in for afternoon tea in your laboratory casually after having made a journey from M87;
2. NO form of entanglement can be confirmed by the observation of only ONE pair of particles. Quantum mechanical experiments are probabilistic in nature, so the only thing you can do is make many measurements and confirm whether or not the correlations between the measured states is statistically significantly higher than the limits laid down by the Bell Inequality for non-entangled particles.

A kind of exception to point 2. is if you measured the state of one photon and confirmed it to have collapsed to, say, left circular polarisation and measured the other also to have collapsed to the same polarisation then you can say that they were, to within your experimental accuracy, not in the entangled state as follows:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,R\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,L\right>\right.\right)$$

So you could conclude, even after one observation, that they probably were not produced in a single interaction producing photons of opposite spin.

But note that this STILL does not rule out entanglement. There is nothing to say that the photons were not in the following nonfactorisable state before the measurement:

$$\frac{1}{2}\left(e^{i\,\phi_1}\,\left|\left.L,\,L\right>\right.+e^{i\,\phi_2}\,\left|\left.R,\,R\right>\right.\right)$$

even though I don't know of any experimental apparatus that could make such an entangled state.