All Questions
Tagged with textbook-and-exercises quantum-state
168
questions
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57
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How I can preform a unitary operation on the third qubit of the GHZ state [closed]
So I create the GHZ state already as the photo below
$$
|\Delta\rangle=\frac1{\sqrt2}(|000\rangle+|111\rangle)
$$
and also I preform a CNOT on the first qubit (as the target qubit), and the second ...
0
votes
0
answers
34
views
How to represent a general 3-qubit state as a symmetric ZX-diagram with 14 parameters?
A general pure 1-qubit state can be written as a ZX-diagram like this:
Correspondingly, for a general pure 2-qubit state:
How can a general pure 3-qubit state be written as a ZX-diagram?
Two things ...
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2
votes
3
answers
158
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Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state?
Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state? Or does a quantum state need to be a superposition of the entire basis, i.e.,
$$ |A\rangle = \frac{1}{...
- 31
-1
votes
1
answer
154
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How to calculate a density matrix of a given circuit?
I want to find the density matrix of the following quantum circuit, is it correct:
[[0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j
0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0....
2
votes
1
answer
237
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How to find the eigenvectors and eigenvalues of a hermitian operator?
While reading Theoretical Minimum by Leonard Susskind, I came across the exercise 3.4 where he asked to find the eigenvalues and the eigenvectors of the matrix that represents the $\sigma_{n}$ ...
- 83
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votes
1
answer
45
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Calculate of theoretical probabilities for the outcomes
I have a $|+\rangle$ state qubit and I measure it in a random basis. The random basis is made with random $\theta$, $\varphi$ and $\lambda$ of $U3$ gate. How can I calculate the theoretical ...
- 9
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53
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Measuring an entangled quantum state
I have this exercise to solve, but I can't figure out how to proceed.
First, I don't think the state proposed is valid (the probabilities don't sum up to 1).
'Secondly, given that it should be an ...
- 29
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votes
1
answer
199
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How to show that the GHZ state is absolutely maximally entangled?
A multipartite state is called absolutely maximally entangled if for its any bipartition the reduced density matrix of smaller part is maximally mixed. Show that GHZ state has this property.
3
votes
2
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123
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
- 57
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votes
1
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300
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The expectation values for the values of both qubits [closed]
Let’s consider the two-qubit state
|Ψ⟩ =(1/2)|00⟩ + i(√3/4)|01⟩ +(3/4)|10⟩.
a) Find the expectation values for the values of both qubits separately.
2
votes
1
answer
85
views
Does the state obtained flipping $a,b$ in the state $(a,b)^T$ have a name?
Suppose we have a qubit with a state vector of $\begin{pmatrix}
a \\
b
\end{pmatrix}
$.
If we flip $a$ with $b$ does the new qubit has a name in relation to the first qubit?
- 151
3
votes
1
answer
133
views
calculate the reduced density matrix of a 2 qubit state and compare the eigenvalues
So I have the exercise to apply a Cz gate to the following 2 Qubit state
$|a\rangle \otimes |b\rangle = (a_0 |0\rangle + a_1 |1\rangle) \otimes (b_0 |0\rangle + b_1 |1\rangle)\\\\$
Afterwards, I ...
- 31
2
votes
0
answers
41
views
Mechanics of expanding projector operator (two - qubits) in basis of traceless Hermitian Paul operators
I am currently on a set of lecture notes which says that for a state vector $| \psi \rangle_{AB}$ describing a tensor product state, its density operator $| \psi \rangle \langle \psi |_{AB}$ can be ...
- 518
2
votes
2
answers
2k
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What is the density matrix of a pure state?
By definition of the density matrix for example the density matrix of $|0\rangle$ state (pure state) is:
$$\rho=|0\rangle \langle 0| =
\begin{pmatrix}
1 & 0 \\
...
- 267
4
votes
2
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260
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Can you distinguish between $|0\rangle, |1\rangle$, and $\frac{1}{\sqrt 2} (|0\rangle + |1\rangle)$?
(A beginner here; possibly a stupid question. Please be gentle. Sorry if I used a wrong tag.)
Suppose that I receive a (classically) random number, which is either $1$ or $2$ or $3$. Depending on this ...
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