I What does the Hadamard correspond to in hardware?

[Kenneth Adam Miller]

As per the title, I'm wondering what exactly is going on at the quantum level that makes entanglement arise - what is the precursor? The hadamard, as I know it, is just a particular set of matrix values that make up an operator. From what I understand, in physics, entanglement is a naturally arising phenomenon stemming from the otherwise would be inconsistent state of the laws of the preservation of momentum. In the case of experiments in which a particle is broken in half before a heat interaction occurs, it is said that their spin state is ambiguous until measured because momentum has to be preserved. Yet, in the moment of interaction in which the particle is struck and broken, momentum is imparted and yet not observed; so it must be distributed across the two particles. That makes sense to me.But exactly what a Hadamard operation is doing to a single electron or quantum particle to me is not clear, because if I understand the state operator correctly, it is operating on the matrix state representation over the discrete information regarding the angles of the qubit (two complex numbers).

 

[PeterDonis]

The hadamard

Do you mean the Hamiltonian? "The hadamard" makes no sense in this context.

 

[Kenneth Adam Miller]

No, I don't mean the Hamiltonian. That is something different; the hadamard is the quantum computing operator responsible for suspending qubits into entanglement.

 

[PeterDonis]

the hadamard is the quantum computing operator responsible for suspending qubits into entanglement

Can you give a reference?

 

[Kenneth Adam Miller]

Sure.

https://en.wikipedia.org/wiki/Hadamard_transform

That's the matrix definition.

 

[PeterDonis]

https://en.wikipedia.org/wiki/Hadamard_transform

That's the matrix definition.

Ok, got it. Are you asking what kind of actual device can implement this transformation? I'm not very knowledgeable about quantum computing hardware, but since the transform amounts to a composition of rotations about two different axes, an appropriate combination of either magnetic fields (if your qubits are electron spins) or polarizers (if your qubits are photon polarizations) ought to do it.

 

[Kenneth Adam Miller]

Yeah, but there's not a fundamental discrepancy between the law of preservation of momentum and the observation of either position or momentum that has clearly been created here in order that entanglement arise. Entanglement is the eventual preservation of that law in the face of an implied ambiguity, if I understand correctly. How does a magnetic field, which actually would affect only the orientation between the fundamental phase and angle of the qubit orientation, not the momentum.

 

[PeterDonis]

but there's not a fundamental discrepancy between the law of preservation of momentum and the observation of either position or momentum that has clearly been created here in order that entanglement arise. Entanglement is the eventual preservation of that law in the face of an implied ambiguity, if I understand correctly.

I don't understand. What "law" and what "discrepancy" are you talking about? Again, do you have a reference for where you are getting this understanding from?

 

[PeterDonis]

In the case of experiments in which a particle is broken in half before a heat interaction occurs

What experiments are you referring to?

 

[Kenneth Adam Miller]

Ok, maybe not experiments exactly, but perhaps learning examples. Hold on, I'm answering your other question.

 

[Kenneth Adam Miller]

OK, so the law of the preservation of energy demands that, as in the original example of the particle being split, that the total momentum before and after the interaction sum up to be the same. So, in the case that a particle is split, each particle of it is now in superposition because the interaction was finite in the step that is affected; position and momentum was computed in terms of the whole particle, and must be redistributed between the two after they have been measured some time after being broken.

 

[PeterDonis]

the original example of the particle being split

Again, can you give a reference? What process are we talking about? Where did you find out about it? You can't just hit quantum particles with a hammer and break them in half. What is this experiment?

 

[Kenneth Adam Miller]

Nah, I don't know the reference off the top of my head. Yeah, it wasn't a hammer, it was firing one particle at another. I know there are more specifics to it, but this is just the way I remember it. I'll see if I can find it somewhere and post it here if I do.