All Questions
38
questions
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49
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Seperable Quantum States
Some similar questions have been ask before, but I still don't really get the definition of seperable states in quantum mechanics.
Consider a bell state of a two qubit system.
\begin{align}
\left|\Psi\...
- 505
1
vote
3
answers
288
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How do I convert this separable state into a product state?
I know two particles in a Bell state cannot be written as a product state as they are entangled. But what if I had a classically correlated state$$\rho = \frac{1}{2}(|11\rangle\langle 11| + |00\rangle\...
- 411
3
votes
0
answers
85
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Constructing wavefunction for a mixed state
This question is somehow the reverse of another question.
If a quantum system $S$ is in a pure state, then we can find a wavefunction that describes $S$. This wavefunction is unique up to a phase ...
- 1,440
1
vote
1
answer
248
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Reduced density matrices and relation to entanglement
I've read that if a state is a product state, the reduced density matrices are pure and if the state is entangled, the reduced density matrices are both mixed.
What would it mean if you had a system ...
- 21
3
votes
3
answers
2k
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Entanglement and density matrices [closed]
Suppose I have a system composed of two subsystems (each is a 2-state system).
Let $$|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle_A \otimes |1\rangle_B - |0\rangle_B \otimes |1\rangle_A)$$ be an ...
4
votes
1
answer
244
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Is a state being unentangled equivalent to statistical independence for all pairs of subsystem observables?
I imagine the answer is yes since, if so, the definition of unentangled is rather non-obvious and yet it gives an operational way to check for statistical independence.
I am working with the standard (...
- 1,095
1
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0
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55
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Is the set of $k$-extendible states compact?
Let 𝑘 ∈ ℕ
. A state 𝜌_𝐴𝐵 on a bipartite Hilbert space A ⊗ B
is 𝑘-extendible with respect to B if there exists a state 𝜌_(𝐴𝐵_𝑘)
on A ⊗ B^(⊗𝑘), which is invariant under any permutation of the ...
- 11
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1
answer
156
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Is entanglement the only way to get mixed state that is consistent with the Schrödinger equation?
If we treat our entire system (say an electron and a bunch of atoms) quantum mechanically then all possible interactions will be unitary transformations. Thus any state that I describe will always be ...
- 9,428
1
vote
0
answers
44
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Representation of $d$-dim maximally mixed state in different bases
Consider the maximally entangled state in $d$ dimensions, $|\Psi\rangle:= \frac{1}{\sqrt{d}} \sum_{i=0}^{d-1} |i,i\rangle^{AB}$, where $|i\rangle^{AB} := |i\rangle^{A}\otimes|i\rangle^{B}$ and $\{|i\...
- 525
1
vote
1
answer
463
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Entanglement Entropy and Entanglement Negativity for pure/mixed separable/entangled state
My question is how is Entanglement Entropy (EE) and Entanglement Negativity (N) related to the combinations of pure/mixed and separable/entangled states? That is for pure separable (PS), pure ...
- 11
11
votes
6
answers
2k
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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, ...
- 245
0
votes
1
answer
260
views
Maximally entangled states of a qutrit system [closed]
How do I construct a qutrit system and then a maximally entangled state for a qutrit system?
- 309
1
vote
2
answers
259
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Intuition/Motivation behind mixed states
I have some confusion regarding pure, mixed and entangled states and I'm trying to gain some clarity on this.
Set up, and my current understanding:
One fundamental distinction I seem to have (please ...
- 593
0
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0
answers
52
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Understanding another Inequality on Entanglement Entropy Found in Hastings Paper on the Area Law
I am currently reading and trying to reproduce the proof found in the following paper by Hastings, in which he proves that the ground state of 1D gapped systems follow an area law. I am trying to ...
- 129
3
votes
1
answer
82
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Understanding an Inequality on Entanglement Entropy Found in Hastings Paper on the Area Law
I am currently reading and trying to reproduce the proof found in the following paper by Hastings, in which he proves that the ground state of 1D gapped systems follow an area law. On the second page, ...
- 129