Probabalistic determination Photon Entaglement

[RobbyQ]

TL;DR

Probabalistic determination Photon Entaglement

If the creation of entangled photons is a probabalistic process and bosons are indistinguishable, how do you know if two photons are entangled and related? For example, in the double slit WPD experiment where a signal and idler entangled photon pair are created. How do you relate them

 

[PeroK]

TL;DR Summary: Probabalistic determination Photon Entaglement

If the creation of entangled photons is a probabalistic process and bosons are indistinguishable, how do you know if two photons are entangled and related? For example, in the double slit WPD experiment where a signal and idler entangled photon pair are created. How do you relate them

Entanglement, theoretically, comes from the conservation laws. That can then be tested. You measure a given quantity on each pair of particles and determine whether they are equal and opposite. If you do that enough times, you are convinced that the particles are entangled. Then, using the same preparation procedure, you do other experiments with the knowledge that you have entangled particles.

 

[PeroK]

PS if you have a random pair of particles, there is no way to know whether they are entangled. You could do one measurement on each of them, but even if that gives an equal and opposite result, that is not conclusive. That could have happened in any case.

 

[RobbyQ]

Entanglement, theoretically, comes from the conservation laws. That can then be tested. You measure a given quantity on each pair of particles and determine whether they are equal and opposite. If you do that enough times, you are convinced that the particles are entangled. Then, using the same preparation procedure, you do other experiments with the knowledge that you have entangled particles.

Thanks Parok
So in the quantum world, measuring just about any property is a probabilistic process eg spin ?

 

[PeroK]

Thanks Parok
So in the quantum world, measuring just about any property is a probabilistic process eg spin ?

In basic QM, there are definite quantities, like mass, charge and total spin. An electron has a given mass, given charge and spin 1/2. A photon has a zero mass, zero charge and spin 1. These are the defining characteristics of these particles.

What isn't well-defined are the dynamic quantities, like position, energy, momentum, angular momentum and spin about a given axis. For a photon, spin is also called polarization.

A particle in QM is defined by its state (also known as the wave-function). In general, even if the state is known, the result of a measurement of a dynamic quantity is probabilistic. The state determines the probability for each possible measurement result. The simplest example is spin about a given axis for an electron. This always has the same magnitude $\frac \hbar 2$, but it can be in either direction, so $\pm \frac \hbar 2$. Also called spin-up and spin-down.

Once you measure the spin, then the state becomes an eigenstate of spin about that axis and further measurements will give the same result (unless there is an external influence like a magnetic field). A measurement of spin about another axis will, however, give $\pm \hbar 2$ with certain probabilities. If the second axis is at right angles to the first, for example, then the probabilities are 1/2 for each possible measurement.

 

[RobbyQ]

In basic QM, there are definite quantities, like mass, charge and total spin. An electron has a given mass, given charge and spin 1/2. A photon has a zero mass, zero charge and spin 1. These are the defining characteristics of these particles.

What isn't well-defined are the dynamic quantities, like position, energy, momentum, angular momentum and spin about a given axis. For a photon, spin is also called polarization.

A particle in QM is defined by its state (also known as the wave-function). In general, even if the state is known, the result of a measurement of a dynamic quantity is probabilistic. The state determines the probability for each possible measurement result. The simplest example is spin about a given axis for an electron. This always has the same magnitude $\frac \hbar 2$, but it can be in either direction, so $\pm \frac \hbar 2$. Also called spin-up and spin-down.

Once you measure the spin, then the state becomes an eigenstate of spin about that axis and further measurements will give the same result (unless there is an external influence like a magnetic field). A measurement of spin about another axis will, however, give $\pm \hbar 2$ with certain probabilities. If the second axis is at right angles to the first, for example, then the probabilities are 1/2 for each possible measurement.

So can a particle of, say, spin 0 decay into two particles of spin +1/2 & -1/2 but still obey the conservation laws where the total spin is still 0 ?

 

[PeroK]

So can a particle of, say, spin 0 decay into two particles of spin +1/2 & -1/2 but still obey the conservation laws where the total spin is still 0 ?

There is no such thing as a spin -1/2 particle. The 1/2 refers to the magnitude of total spin, which is always positive. That said, two spin 1/2 particles can be in the singlet state. This is an entangled state with a total spin of 0. If two such particles are created from a system with zero spin, then the conservation law for spin about any axis implies that they must be in the (entangled) singlet state. This guarantees that, if measured about the same axis, they must have opposite spin. I.e. one would be $\frac \hbar 2$ and the other $-\frac \hbar 2$.

PS a spin 1/2 particle has a total spin of $\frac {\sqrt 3} 2 \hbar$.