All Questions
5
questions
3
votes
1
answer
139
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Is there a relation between some kind of distance and the Schmidt basis?
Consider two bipartite quantum states $|\phi\rangle^{AB}$ and $|\psi\rangle^{AB}$ (in a finite dimensional Hilbert space $\mathcal H_A\otimes \mathcal H_B$), such that
$$\| |\phi\rangle\langle\phi|^{...
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1
vote
5
answers
1k
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Mathematical explanation of bra-ket notation in quantum mechanics
$\newcommand{\hp}[1]{\hphantom{#1}}$
We have the entangled state of two pairs of qubits:
$$
|\psi \rangle =\frac{1}{2}|0011\rangle-\frac{1}{2}|0110\rangle-\frac{1}{2}|1001\rangle+\frac{1}{2}|1100\...
- 253
31
votes
7
answers
7k
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What is the actual use of Hilbert spaces in quantum mechanics?
I'm slowly learning the quirks of quantum mechanics. One thing tripping me up is... while (I think) I grasp the concept, most texts and sources speak of how Hilbert spaces/linear algebra are so useful ...
- 531
1
vote
1
answer
2k
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Schmidt decomposition of entangled state [closed]
I have a problem with some homework our teacher assigned. I have to find the Schmidt decomposition of the entangled state
$$\lvert\psi\rangle_{A,B}=\frac{1}{2}\lvert0\rangle_{A}\lvert0\rangle_{B}-\...
6
votes
2
answers
674
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Why is the dimension of the set separable states $\dim\mathcal H_1+\dim\mathcal H_2$?
Please can you help me to understand how the dimension of the set of separable states is $\dim \cal H_1 + \dim \cal H_2$?
This is the relevant passage:
So far, we have assumed implicitly that the ...
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