4
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Accepted
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 ...
- 848
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Accepted
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 ...
- 5,158
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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 ...
- 55.7k
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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 $\phi_1(x)$...
- 13.5k
2
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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 ...
- 5,354
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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 ...
- 1,311
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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):
$$ |GHZ\rangle = \frac{1}{\sqrt{2}} \...
- 1,709
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vote
Accepted
How does this measurement in the Hadamard basis look like?
Answer refined based on updated question
Your updated question boils down to something like “if we take a Hadamard transform of a superposition of two basis states and measure, why is our string ...
- 10.7k
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Accepted
How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
If you consider the state
$$\Omega_- = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle).\tag{1}$$
you will find that there is NO violation. Let me show this. Note that the approach I will use for solving ...
- 126
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
From your current description, it seems that you have found each eigenvector $\{|v_1\rangle,...,|v_4\rangle\}$ and its associated eigenvalue $\lambda_1,...,\lambda_4$. These eigenvalues represent the ...
- 93
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Accepted
How to combine measurement of each term in Hamiltonian $H = aH_1 + bH_2$ to get final results?
Community Wiki
It seems like you wish to perform a "Local Hamiltonian Simulation" where your Hamiltonian $H$ is the sum of two separate terms:
$$H=aH_1+bH_2.$$
That is, you wish to ...
Only top scored, non community-wiki answers of a minimum length are eligible