Questions tagged [textbook-and-exercises]
Applies to questions of primarily educational value - styled in the format similar to that found in textbook exercises. This tag should be applied to questions that are (1) stated in the form of an exercise and (2) at the level of basic quantum information textbooks.
675
questions
0
votes
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Quantum Cryptography without Bell's Theorem -- Brassard - Bennett - Mermin
It is an old paper but I'm trying to understand one of their argument. They say that if
$$U|u\rangle |a\rangle = |u\rangle |a^\prime\rangle \ \ \ \mathrm{and} \ \ \ U|v\rangle |a\rangle = |v\rangle |a^...
- 173
3
votes
1
answer
330
views
Wong's "Introduction to Classical and Quantum Computing" Exercise 7.23
I am currently working my way through "Introduction to Classical and Quantum Computing" by Thomas Wong. I am trying to solve the following problem:
Exercise 7.23. Answer the following ...
- 81
1
vote
3
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59
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Intro book on classical and quantum computing by Thomas G Wong
Looking at his book, and am obviously new to studying this. Could someone help explain to me how the truth table is valid here?
To my understanding, when $C=0$, the circuit behaves like a reversible ...
- 11
2
votes
1
answer
163
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Wong's "Introduction to Classical and Quantum Computing" Exercise 7.20
I am currently working my way through "Introduction to Classical and Quantum Computing" by Thomas Wong. I am trying to solve the following problem on Simon's Algorithm:
Exercise 7.20. You ...
- 81
0
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0
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57
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How I can preform a unitary operation on the third qubit of the GHZ state [closed]
So I create the GHZ state already as the photo below
$$
|\Delta\rangle=\frac1{\sqrt2}(|000\rangle+|111\rangle)
$$
and also I preform a CNOT on the first qubit (as the target qubit), and the second ...
1
vote
2
answers
157
views
If eigenvalues of two matrices are equal then the matrices are equal?
Suppose $k_i$ and $f_i$ are eigenvalues of two density matrices A and B,
If $k_i=f_i$ then A=B?
If the answer is no, under which conditions the statement holds?
- 761
2
votes
2
answers
84
views
Show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \right\rangle$ is unitary [duplicate]
I am reading Quantum Computation and Quantum Information by Chuang and Nielsen and they claim that it is easy to show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \...
- 121
-1
votes
1
answer
106
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Hong Ou Mandel interference and bell basis measurment
It is well known that using Hong Ou Mandel interference in polarization one can only detect 2 out of the 4 bell states($|\psi^+\rangle$ and $|\psi^-\rangle$ can be detected but $|\phi^+\rangle$ and $|\...
0
votes
0
answers
34
views
How to represent a general 3-qubit state as a symmetric ZX-diagram with 14 parameters?
A general pure 1-qubit state can be written as a ZX-diagram like this:
Correspondingly, for a general pure 2-qubit state:
How can a general pure 3-qubit state be written as a ZX-diagram?
Two things ...
- 745
1
vote
1
answer
67
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Clarification about the Alberti's Theorem proof given by Watrous in his condensed lecture notes
In the John Watrous condensed TQI lecture notes, an alternative proof of the Alberti's Theorem is given. He use an auxiliary lemma that states;
Lemma 4.9. Let $P \in Pos(X)$. It holds that $${inf}_{R\...
- 63
5
votes
2
answers
403
views
Represent Hadamard gate in terms of rotations and reflections in Bloch sphere
I read in a book that any single qubit operation can be decomposed as
$$
\bf{U} =e^{i\gamma}\begin{pmatrix}e^{-i\phi/2}&0\\ 0&e^{i\phi/2}\end{pmatrix}\begin{pmatrix}\cos{\theta/2}&-\sin{\...
- 51
0
votes
1
answer
56
views
How does measuring a density matrix give Kraus operators?
I am trying to complete this exercise regarding noisy channels. I need to measure a density matrix to get the Kraus operators. However, if I measure, I only get scalars. Can someone please explain how ...
- 163
4
votes
2
answers
82
views
Why do minimal ensemble decompositions for $\rho$ contain $|\psi⟩\in{\rm supp}(\rho)$ with probability $1/\langle\psi|\rho^{-1}|\psi⟩?$
I came across the following exercise (2.73) in Nielsen & Chuang and am trying to understand it intuitively.
Here is my reasoning of what is going on:
The purpose of this exercise:
Let’s say we are ...
- 163
1
vote
2
answers
56
views
What is meant with "different ensembles can give rise to the same density matrix?"
I am reading the Nielsen & Chuang section on density matrices and I don't understand the example given to demonstrate a concept. Here is what I am reading:
First, they said these two different ...
- 163
1
vote
1
answer
53
views
Finding the effect of conjugate transpose on a state $|b\rangle$
Say that I have a unitary gate $U$ such that $U|b\rangle=|b+1$ mod $N\rangle$. How would I go about finding $U^\dagger|b\rangle$?
- 63