All Questions
Tagged with quantum-entanglement homework-and-exercises
38
questions
2
votes
2
answers
102
views
How to determine parameters such that the state $|\psi\rangle=\frac1{\sqrt2}|+\rangle|+\rangle+a|+\rangle|x+\rangle+b|-\rangle|-\rangle$ is separable?
Suppose that two spin-1/2 are in the state:
$$ |\psi \rangle = \frac{1}{\sqrt{2}} |+\rangle|+\rangle + a|+\rangle|x+\rangle + b|-\rangle|-\rangle $$
and we want to find values for a & b such that ...
- 189
3
votes
1
answer
88
views
Why is the entanglement of formation upper bounded by the Schmidt number?
I have read many times in several articles (such as https://arxiv.org/abs/1609.05033) that the entanglement of formation EoF puts a lower bound on entanglement dimensionality $d$ (i.e., the Schmidt ...
- 237
1
vote
1
answer
66
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If you measure one "share" of an entangled pair, will the resulting pair be a product state?
If you do a partial measurement on one "share" of en entangled pair, will the resulting pair no longer be entangled, i.e will be a product state?
- 245
0
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40
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Why aren't states with 3 basis vectors considered entanglements in two qubit system?
I am going to take out normalization factors for simplicity.
$$|00⟩+|11⟩$$
$$|00⟩−|11⟩$$
$$|10⟩+|01⟩$$
$$|10⟩−|01⟩$$
I can see why these states are entangled but I don't see why the following states ...
2
votes
1
answer
493
views
How to compute the Schmidt decomposition of a bipartite pure state?
I'm trying to work out the entropy of entanglement of my state but I'm struggling to put it into a Schmidt decomposition, i.e. in the form:
$\sum_i \alpha_i |u_i \rangle |v_i \rangle$.
Currently I ...
0
votes
2
answers
46
views
What is the dimension of two quantum systems with bases $\{a_1,a_2\}$ and $\{b_1,b_2,b_3\}$, combined? [closed]
Quantum system A has a basis $\{a_1, a_2\}$. System B has a basis $\{b_1, b_2, b_3\}$. A and B evolve according to their own Hamiltonian and do not interact at all. If I consider A and B as one large ...
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-1
votes
1
answer
151
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Time evolution for one photon using beam splitter [closed]
One option that seems to work is that if you have exactly 1 photon, you can work out your coefficients by representing the exponential matrix $e^{−iHt}$ as a Taylor series, and you end up with ...
- 19
0
votes
1
answer
221
views
How to take partial inner product between tensor product states and GHZ state?
I am trying to solve some problems in which 3 people (Alice, Bob and Charlie) share 3 photons entangled in the state $|GHZ\rangle$ and Alice and Bob perform some joint measurement on $|GHZ\rangle$. I ...
- 103
2
votes
1
answer
433
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How do I compute the partial trace of $\sqrt{p}|0\rangle_a|0\rangle_b+\sqrt{1-p}|1\rangle_a |1\rangle_b$?
Here I have a two pure state system composed from systems A and B:
$$\Psi_{ab} = \sqrt{p}\, |0\rangle_a |0\rangle_b + \sqrt{1-p}\, |1\rangle_a |1\rangle_b $$
How do I extract system A in matrix form ...
3
votes
0
answers
115
views
How does this quantum circuit work? [closed]
I am getting a bit confused about how to trace through a quantum circuit.
So, for example, if you have the circuit below:
I know that the first gate would split an arbitrary state alpha|0> + beta|...
- 39
1
vote
1
answer
327
views
Integration with respect to Haar measure and reduced density matrix [closed]
Consider a bipartite system $\mathcal{H}_A \otimes \mathcal{H}_B$, with $|A|,|B|>>1$ and not necceserly $|A|=|B|$.
Following Jerusalem Lectures on Black Holes and Quantum Information (eq. 5.8) ...
- 339
2
votes
1
answer
157
views
How do I show the separability of this density matrix?
I am stuck since a longer time regarding this exercise where I need to work with a density matrix of the given form
$$\displaystyle \rho_{AB}(X)= \frac{1}{N+\text{tr}X^2}\left( {\begin{array}{cc}
...
2
votes
1
answer
716
views
3 qubit maximally entangled state $\frac{1}{2}(|000\rangle + |110\rangle+ |011\rangle + |101\rangle)$
Is there any general criteria for maximal entanglement in 3 qubit system. I have encountered this problem-"Suppose you have a state $\frac{1}{2}(|000\rangle + |110\rangle+ |011\rangle + |101\...
1
vote
1
answer
159
views
Why can any pure bipartite state be written in the Schmidt decomposition as $|\Psi\rangle=\cos\theta|00\rangle+\sin\theta|11\rangle$?
The beginning of this paper (pg.no. 1) on generalised Schmidt decomposition of three qubit states mentions the following:
The Schmidt decomposition allows one to write any pure state of a bipartitie ...
- 21
1
vote
1
answer
98
views
Find the normalized state and function such that the equation holds for arbitrary unitary matrix [closed]
I have been recently puzzled with a problem I do not know how to solve. Here is the setting and some of my thoughts on the problem.
Given:
Let us denote the set of all unitary $d \times d$ matrices ...
