B How to create quantum entangled electrons

[IsaiahvH]

I understand that one way of creating quantum entangled electrons is by splitting a Cooper pair. Is then their spin property used in the measurement, as this must always sum to $0$ for a Cooper pair?
If that is the case, do quantum entangled electrons only exist in the singlet state, where the spin is always opposite to one another?
$$\frac{1}{\sqrt{2}}(\left|01\right> \pm \left|10 \right>)$$

Are there other methods of creating quantum entangled electrons?

 

[A. Neumaier]

Any atom (except for hydrogen atoms) is surrounded by several entangled electrons.

 

[PeroK]

I understand that one way of creating quantum entangled electrons is by splitting a Cooper pair. Is then their spin property used in the measurement, as this must always sum to $0$ for a Cooper pair?
If that is the case, do quantum entangled electrons only exist in the singlet state, where the spin is always opposite to one another?
$$\frac{1}{\sqrt{2}}(\left|01\right> \pm \left|10 \right>)$$

Are there other methods of creating quantum entangled electrons?

It seems to me you may be getting the terminology mixed up here.

The singlet state is $|0 \ 0\rangle = \frac{1}{\sqrt{2}} (\uparrow \downarrow - \downarrow \uparrow)$.

The triplet is a combination of 3 states, so called because they share a common value for total spin:

$|1 \ 1\rangle =\ \uparrow \uparrow$
$|1 \ 0\rangle = \frac{1}{\sqrt{2}} (\uparrow \downarrow + \downarrow \uparrow)$
$|1 \ -\!1\rangle =\ \downarrow \downarrow$

 

[Strilanc]

It seems to me you may be getting the terminology mixed up here.

The singlet state is $|0 \ 0\rangle = \frac{1}{\sqrt{2}} (\uparrow \downarrow - \downarrow \uparrow)$.

The triplet is a combination of 3 states, so called because they share a common value for total spin:

$|1 \ 1\rangle =\ \uparrow \uparrow$
$|1 \ 0\rangle = \frac{1}{\sqrt{2}} (\uparrow \downarrow + \downarrow \uparrow)$
$|1 \ -\!1\rangle =\ \downarrow \downarrow$

Where are you getting that notation from? In quantum information the singlet state is $\frac{1}{\sqrt{2}} \left( |01\rangle - |10\rangle \right)$. Certainly not $|00\rangle$. That's the "both qubits are in the off state" state.

 

[PeroK]

Where are you getting that notation from? In quantum information the singlet state is $\frac{1}{\sqrt{2}} \left( |01\rangle - |10\rangle \right)$. Certainly not $|00\rangle$. That's the "both qubits are in the off state" state.

I thought we were talking about electrons and that that notation was fairly standard.

 

[Mentz114]

..
Are there other methods of creating quantum entangled electrons?

Yes there is another way. Two entangled photons can interact with two electorns and swap the entanglement to the electrons. I haven't got the details to hand but I'll search.

 

[Nugatory]

Where are you getting that notation from? In quantum information the singlet state is $\frac{1}{\sqrt{2}} \left( |01\rangle - |10\rangle \right)$. Certainly not $|00\rangle$. That's the "both qubits are in the off state" state.

I believe that @PeroK is using a convention in which the spin state of the individual particles is represented with up and down arrows, and a ket containing two numbers is the state with total spin given by the first number and projection of the total spin by the second. That's not the convention being used elsewhere in this thread, and I don't know how common it is, but I'm pretty sure it was the one used back when I learned about quantum spin.

 

[secur]

I understand that one way of creating quantum entangled electrons is by splitting a Cooper pair. Is then their spin property used in the measurement, as this must always sum to $0$ for a Cooper pair?
If that is the case, do quantum entangled electrons only exist in the singlet state, where the spin is always opposite to one another?
$$\frac{1}{\sqrt{2}}(\left|01\right> \pm \left|10 \right>)$$
Are there other methods of creating quantum entangled electrons?

Entangled electrons don't only exist in the singlet state. They can also have, for instance, positively correlated spins.

There are a number of methods of creating entangled electrons and particles. Unfortunately I don't know what they are, ask an experimenter. For photons, there's parametric downconversion, SPS cascades, annihilation of spin-zero particle states into two gamma rays, etc.

Finally, I'm supposing you mean to "create" the pair in the lab for entanglement experiments. In "the wild" they exist everywhere. As @A. Neumaier says, they exist in an atom. For instance whenever an orbit has two electrons they must have opposite spins. Generally whenever two particles interact in any way they become entangled (maybe there are exceptions). For instance if they scatter off each other, the sum of their outgoing momenta must equal sum of ingoing momenta - they're entangled.