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No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited revisited

I think what you asking about is the following setting: you are given a qubit which is either $|\psi\rangle$ or $|\psi'\rangle$ with are not orthogonal. You know what those two possible states are, ...
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No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited revisited

The crucial point about the no-cloning theorem is (as you already suspect) the basis choice. You can always find a specific cloning machine for a specific basis, but you cannot find a general cloning ...
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Why does it matter that Schmidt number is invariant under unitary transformations?

Regarding your first question. Consider having the following bipartite state:  |\psi\rangle_{AB} = \frac{1}{2}|00\rangle_A|00\rangle_B+ \frac{\sqrt{3}}{6}|01\rangle_A|01\rangle_B+ \frac{\sqrt{6}}{6}...
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Why does it matter that Schmidt number is invariant under unitary transformations?

Crucially, "the Schmidt number is preserved under unitary transformations on system A or system B alone". So Schmidt numbers are invariant under local operations $U_A\otimes U_B$, but not ...
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Why do we need/have the operator sum representation (Kraus representation)?

To add to Daniele's and Frederik's answers: the operator sum representation is even more useful than the Nielson and Chuang derivation might suggest - though, the derivation is very helpful from a ...
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To add to Daniele's answer, $E_k$ is an operator—and not a scalar—because the notation in Nielsen & Chuang is sloppy. What is meant is that $E_k=\iota_k^\dagger U\iota_0$ where $\iota_k:\mathbb C^... • 1,961 2 votes Why do we need/have the operator sum representation (Kraus representation)? The formalism is useful to describe a noisy transformation$\mathcal{E}$only in the domain of a system of interest$\mathcal{H}$. According to the book, you can select an orthogonal bases$\{e_i\}_i$... • 1,968 2 votes What is meant with "different ensembles can give rise to the same density matrix?" An ensemble in this context is a set of states with attached probabilities. In your example the ensembles would be written as$\{(\frac12,|a\rangle\langle a|),(\frac12,|b\rangle\langle b|)\}$and$\{(\...
The two ensembles are $|0\rangle, |1\rangle$ and $|a\rangle, |b\rangle$. The point of this example is to show you that the same density matrix \$\rho = \begin{pmatrix} 3/4 & 0 \\ 0 & 1/4 \end{...