$ |\psi\rangle = \prod_{i=1}^{N}|s_{i}\rangle $ where, $|s_{i}\rangle = \cos\left (\frac{\theta_{i}}{2}\right )|\uparrow_{i}\rangle + \exp{(i\phi_{i})}\sin\left (\frac{\theta_{i}}{2}\right )|\downarrow_{i}\rangle$. $\theta_{i}$ and $\phi_{i}$ are randomly chosen from the intervals $[0,\pi]$ and $[0,2\pi]$ respectively. Can this random product state be written as an matrix product state?

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    $\begingroup$ In fact it can with unit bond dimension... $\endgroup$ – Ryan Thorngren Oct 1 at 17:17
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    $\begingroup$ Sure it can. Your amplitudes are the respective 1x1 matrices. $\endgroup$ – Zarathustra Oct 1 at 17:34
  • $\begingroup$ You have been posting questions about MPS already a year ago. By now you should know enough about them to make your question more precise. What are your thoughts, and where are you struggling? $\endgroup$ – Norbert Schuch Oct 1 at 18:25

Hint: $A_1^{\uparrow} = \begin{pmatrix}\cos\left(\frac{\theta_1}{2}\right)\end{pmatrix}$, $A_1^{\downarrow} = \begin{pmatrix}e^{i\phi_1}\sin\left(\frac{\theta_1}{2}\right)\end{pmatrix}$

  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$ – Aaron Stevens Oct 1 at 22:00
  • $\begingroup$ I disagree, but ok. $\endgroup$ – d_b Oct 1 at 23:13

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