# Does a c-not gate conserve angular momentum?

1. Mar 8, 2009

### Phrak

Does a c-not gate conserve angular momentum?

2. Mar 8, 2009

### Phrak

Re: C-not

cnot(control, target)
--------------------------
cnot(|0>, |0>) = |0>, |0>
cnot(|0>, |1>) = |0>, |1>
cnot(|1>, |0>) = |1>, |1>
cnot(|1>, |1>) = |1>, |0>

3. Mar 9, 2009

### Manchot

Re: C-not

Your question doesn't make sense. A CNOT gate is just a unitary operator acting on an arbitrary tensor product of two-dimensional Hilbert spaces. To talk about physical quantities like angular momentum, you need to specify the precise implementation of the qubits in the system. For example, if you're using photons to represent qubits, it obviously doesn't make a whole lot of sense to talk about angular momentum.

4. Mar 10, 2009

### Phrak

Re: C-not

Photons have angular momentum. The kets represent electon spin states, up and down.

Last edited: Mar 10, 2009
5. Mar 12, 2009

### Phrak

Re: C-not

I don't see why this should be a hard or uninteresting question.

Either 1) I don't get it, and it's nonsense to talk about the total angular momentum of two entangled electrons,

Or 2) spin states of two electons acted upon by a Cnot gate have their spin states entangled with the gate.

Or 3) I'm completely lost and will never understand quantum mechanics, and so why bother.

6. Mar 12, 2009

### jensa

Re: C-not

I think most people find this uninteresting (myself included). Maybe if you could tell us why you are interested in this others would be interested too. What if it is conserved? What if it isnt?

If you think of a single qubit (spin), an arbitrary single qubit gate is designed to change the spin (perform unitary rotation of the spin). So obviously angular momentum is not conserved.

If you consider two qubits and perform a controlled not gate, or a controlled-anything gate you change the spin of one of the qubits depending on the state of the other. I'm pretty sure the angular momentum is not conserved under such an operation. And why should it be? I would guess you make the appropriate manipulations by applying magnetic fields so there is no spin-rot symmetry or anything like that.

Not a quality answer but maybe it is something.

7. Mar 12, 2009

### alxm

Re: C-not

Of course angular momentum, in the bigger context, is conserved. A real functioning gate is not an isolated system.

http://prola.aps.org/abstract/PRL/v75/i25/p4714_1
For instance, is being pumped with a laser. That's where any change in total angular momentum is being supplied from.

8. Mar 12, 2009

### jensa

Re: C-not

Yes after writing my post I realized that Phrak maybe was concerned with the conservation of total angular momentum of the universe. But obviously this is how we always model systems acted upon by external means. We supply energy, angular momentum, etc, and thus break certain symmetries...

9. Mar 12, 2009

### Phrak

Re: C-not

That's true, jensa, I haven't made it very interesting.

Thanks, alxm. I'll try to get ahold of the article.

To understand decoherence, we need to know where qbits are entangled, and how.

If I get this correctly, after the operation of a cnot on the control and target bits, the spin states of control and target are not the only spin states effected, but the spin states of the gate, itself is altered. This would mean that the truth table of a cnot gate is incomplete. If it's incomplete, how is it reversible?

If the operation is preformed by bathing in a source of radiation, the source of radiation is now entangled with the two qbits, as well as the walls of the container, where any stimulated radiation from the qbits may be absored. Radiation source and sink are part of the gate.

Last edited: Mar 12, 2009