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How to properly understand Born's rule as written in the Feynman Lectures?

$\newcommand{\complexes}{\mathbb{C}}$I'm trying to make sense of Born's rule involving a single qubit. Probably, I'm mixing apples and oranges here, but I can't tell where or why. In "The ...
hft's user avatar
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Is possible to write a separable state as a finite or countable infinite sum of product states?

Yes, you can always write an integral of separable states as a (finite) convex combination of product states, owing to the fact that the set of separable states is compact. A quick way to see this is ...
John Watrous's user avatar
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3 votes

Which single-qubit mixed states work for magic state distillation?

I've not kept sufficiently up to date with the most recent literature, however, here are some partial results: Along certain axes of the Bloch sphere, the divide between the octahedron and the ...
DaftWullie's user avatar
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How to properly understand Born's rule as written in the Feynman Lectures?

The $\phi_1$ and $\phi_2$ are not just "numbers" but "wavefunctions". For the two-slit experiment, they depend on a position, $x$, so the "functions" look like $\phi_1(x)$...
user1271772's user avatar
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2 votes

quantum generalisation of random variables

If I understand your question, the way a classical random variable $X$ with support $\left[2^n\right]=\left\{0,\cdots,2^n-1\right\}$ is represented in quantum information is via a diagonal density ...
Tristan Nemoz's user avatar
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Is the full quantum circuit always in a pure state?

Yes. If you prepare a state, say $|0\rangle ^{\otimes n}$ (or any pure state in general) and only perform quantum gates (which are unitary operations) and qubits are perfectly isolated (there are no ...
FDGod's user avatar
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How to show that the GHZ state is absolutely maximally entangled?

I assume that you talk about the standard case of a $3$-qubit GHZ state (the generalized versions of $n$-qubit GHZ states are not absolutely maximally entangled): $$ |GHZ\rangle = \frac{1}{\sqrt{2}} \...
Ohad's user avatar
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How does this measurement in the Hadamard basis look like?

Answer refined based on updated question Your updated question boils down to something like “if we take a Hadamard transform of a superposition of two basis states and measure, why is our string ...
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?

If you consider the state $$\Omega_- = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle).\tag{1}$$ you will find that there is NO violation. Let me show this. Note that the approach I will use for solving ...
Alex's user avatar
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?

From your current description, it seems that you have found each eigenvector $\{|v_1\rangle,...,|v_4\rangle\}$ and its associated eigenvalue $\lambda_1,...,\lambda_4$. These eigenvalues represent the ...
Kilian's user avatar
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How to combine measurement of each term in Hamiltonian $H = aH_1 + bH_2$ to get final results?

Community Wiki It seems like you wish to perform a "Local Hamiltonian Simulation" where your Hamiltonian $H$ is the sum of two separate terms: $$H=aH_1+bH_2.$$ That is, you wish to ...

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