# Tag Info

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First of all, here's a short disclaimer: I'm not an in-depth expert in this field, I'm just currently getting in contact with tomography more and more often :) So take the following with a grain of salt. It might be incomplete in the sense that better results have been shown somewhere. We consider the problem of reconstructing a $d$-dimensional quantum state ...

4

Denote the projections onto basis elements by $P_j^{(k)}=|u_j^{(k)}\rangle\langle u_j^{(k)}|$, where superscript indexes different bases. Tomography of a density matrix $\rho$ gives us probabilities $\text{Tr}(\rho P_j^{(k)})$. This is actually a value of the Hilbert-Schmidt inner product between $\rho$ and $P_j^{(k)}$ in the space $L(\mathcal{H})$ $-$ the ...

3

There is no general exact formula for $N(\epsilon, d)$ and some special cases (for example SIC-POVM) is an area of active research. However there is a Welch bound that gives $\epsilon^2 \ge \frac{n-d}{d(n-1)}, n=N(\epsilon, d)$ and hence bounds $N(\epsilon, d)$ from above.

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This seems like it should be a known mathematical property of Hilbert spaces, but I can't immediately lay my hand on any such result. In lieu of that, this is very far from an answer to your question, but it perhaps indicates the difficulty of (some of) what you're asking... First, perhaps we can clarify your problem statement. I assume you mean  |\langle ...

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