All Questions
Tagged with quantum-entanglement hilbert-space
163
questions
31
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7
answers
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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 ...
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23
votes
6
answers
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How do we know that entanglement allows measurement to instantly change the other particle's state? [duplicate]
I have never found experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than just being revealed.
Using the spin up spin down ...
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22
votes
3
answers
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What is a completely positive map *physically*?
This can be considered as a continuation of this question.
What does it mean to be a completely positive map, from a Physics point of view?
A positive map $h:\mathcal{B(H)}\rightarrow\mathcal{B(K)}$ ...
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19
votes
1
answer
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Is purification physically meaningful?
Consider a quantum system with Hilbert space $\mathscr{H}$ and suppose the quantum state is specified by a density operator $\rho$. Since it is Hermitian, it has a spectral decomposition: $$\rho = \...
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18
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2
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What Shannon channel capacity bound is associated to two coupled spins?
The question asked is:
What is the Shannon channel capacity $C$ that is naturally associated to the two-spin quantum Hamiltonian $H = \boldsymbol{L\cdot S}$?
This question arises with a view ...
John Sidles
16
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5
answers
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How do tensor products and direct sums fit into quantum mechanics?
I understand that at times tensor products or direct sums are taken between Hilbert spaces in quantum mechanics. I don't, however, know when this can be done or when it should be done. I would like ...
user113773
16
votes
3
answers
2k
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Entangled or unentangled?
I got a little puzzled when thinking about two entangled fermions.
Say that we have a Hilbert space in which we have two fermionic orbitals $a$ and $b$. Then the Hilbert space $H$'s dimension is just ...
- 4,420
14
votes
2
answers
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Implications of MIP*=RE for physics?
Background
Earlier this month (Jan 2020) a pre-print was posted to the arXiv claiming to have proved the equivalence of the complexity classes $\mathrm{MIP}^{*}$ and $\mathrm{RE}$ (see below for ...
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11
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6
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Why do we need mixed states in quantum mechanics?
I am trying to understand the necessity of density matrices and the notion of "mixed states" in quantum mechanics (I read all the other posts about this, I promise).
As far as I understand, ...
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11
votes
3
answers
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What is the minimum number of separable pure states needed to decompose arbitrary separable states?
Consider a separable state $\rho$ living in a tensor product space $\mathcal H\otimes\mathcal H'$, with $\mathcal H$ and $\mathcal H'$ of dimensions $D$ and $D'$, respectively.
If $\rho$ is separable, ...
- 14.8k
10
votes
2
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Does correlation of the measurement outcomes imply that a state is entangled?
As per Wikipedia:
Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot ...
- 203
9
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3
answers
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What is quantum entanglement? [closed]
What is quantum entanglement?
Please be pedagogical.
Edit: I have updated my background under my profile.
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9
votes
2
answers
2k
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How are entangled states created?
I understand that when I have two separate states that their combination state increases the Hilbert Space to
$|\psi_1\rangle \otimes |\psi_2\rangle$
For example, looking at a simple example where ...
- 2,193
9
votes
1
answer
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Methods to distinguish between pure/mixed states and entangled/separable states
I'm a little confused about how we can distinguish between pure/mixed states and entangled/separable states and I would really appreciate some help!
I understand a density operator $\rho$ represents ...
- 623
8
votes
1
answer
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Quantum circuit for a $3$-qubit $|W \rangle$ state [closed]
Can someone specify a quantum circuit that will deterministically output the $3$-qubit $|W \rangle$ state, if the input to the circuit is $|0,0,0 \rangle$? Or, is there a quantum circuit with a ...
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