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 Post subject: Question about entanglement
PostPosted: Fri, 2 Mar 2012 22:11:00 UTC 
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Ok so this is a pretty straightforward question. Entanglement states that if you apply an outside force to two atoms, they will become entangled and the second atom will assume the properties of the first atom. Once the first atom chooses a spin, the second atom will immediately choose the opposite spin. Will the second atom ever choose a spin and affect the first atom? Or is it a one-way ordeal? Also, how does this really solve the superposition issue?

I'm currently writing a paper on quantum computing, and need some basic info on quantum mechanics. My paper is not really on the quantum physics, but I need a little bit of information. And these two questions have had me kind of stumped and I'm having no luck researching them.


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 Post subject: Re: Question about entanglement
PostPosted: Sat, 3 Mar 2012 06:01:43 UTC 
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ResidentBiscuit wrote:
Ok so this is a pretty straightforward question. Entanglement states that if you apply an outside force to two atoms, they will become entangled and the second atom will assume the properties of the first atom. Once the first atom chooses a spin, the second atom will immediately choose the opposite spin. Will the second atom ever choose a spin and affect the first atom? Or is it a one-way ordeal? Also, how does this really solve the superposition issue?

I'm currently writing a paper on quantum computing, and need some basic info on quantum mechanics. My paper is not really on the quantum physics, but I need a little bit of information. And these two questions have had me kind of stumped and I'm having no luck researching them.


No! You only have two feasible states \mid\uparrow\downarrow\rangle,\mid\downarrow\uparrow\rangle in the tensor product \mathcal{H}\otimes\mathcal{H}, not four, and of course the wavefunction evolves according to the Schr\"{o}dinger equation.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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