user1936752
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Is the quantum state fidelity defined as $F(\rho, \sigma)=\text{tr}\sqrt{\rho^{1/2}\sigma\rho^{1/2}}$ or its square?
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4 votes

Both definitions are used and authors usually make it clear which one they mean. Wikipedia also points this out under the Alternative Defintion section.

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What's the interpretation of the eigenvalues of qubit's projective operators?
Accepted answer
2 votes

The eigenvalues are just labels for the outcomes of the measurement. They don't necessarily have any physical meaning. See this answer for a more detailed understanding.

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Is the set of density operators invariant under the induced action of the unitary group?
1 votes

I'm not sure what $End(H)$ is but here is a proof that unitaries take density operators to density operators. Let $X$ be a positive semidefinite matrix with unit trace. We have to show that for a ...

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Bounding diamond norm distance using probability of error in transmission of classical information
0 votes

Let us pick a basis for the Hilbert space $\mathcal{H}$ of dimension $d$ to be $\{\vert i\rangle\}$ and let $\mathcal{P}: \mathcal{H}\rightarrow\mathcal{H}$ be the dephasing map given by $$\mathcal{P}:...

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The correct set of measurement operators on a mutiple qubit system
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A valid measurement consists of operators $\{M_k\}$ such that $\sum_k M^\dagger_k M_k = I$. You need appropriate normalization factors in front for both cases but since $P_i^\dagger P_i = P_i$ and $...

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