All Questions
Tagged with textbook-and-exercises terminology-and-notation
26
questions
0
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1
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23
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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
1
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1
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102
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Can a density operator be written equivalently as $\rho=\sum_i p_i|\psi_i〉\!\langle\psi_i|$ and $\rho=\sum_i\lambda_i|\psi_i\rangle\!\langle\psi_i|$?
My doubt arises from page 99, 101 of the book Quantum Computation and Quantum Information by Michael A.Nielson and Issac L.Chung.
Let {${p_{i}, | \psi_{i} \rangle }$} be an ensemble of pure states.
...
- 518
0
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1
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66
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What does the notation $\sum_\lambda \lambda \left | \lambda \right > \left < \lambda \right |$ mean?
In many places, I see a form of representing a matrix with:
$A = \sum_\lambda \lambda \left | \lambda \right> \left < \lambda \right |$
Where $\lambda$ is an eigenvalue, and $\left | \lambda \...
- 423
6
votes
1
answer
3k
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What is the difference between "maximally entangled" and "entangled" states?
when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
- 577
-1
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1
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76
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Is the $|00\rangle$ basis the same as the $|\phi^+\rangle$ basis?
I am working on a problem where I have 4 entangled qubits. I want to trace out 2nd and 3rd qubits by projecting them onto the $|00\rangle$ basis. Is the $|00\rangle$ basis the same as the $|\phi^+\...
- 115
3
votes
2
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123
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For two-qubit systems, do we have $\langle 01|01\rangle = \langle 0|0\rangle\langle 1|1\rangle$?
I am new to quantum computing and I want to know the following: If I have a 2 qubit system in state e.g. $\left|01\right>$ and I want to calculate the probability of measuring e.g. $\left<01\...
- 133
3
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1
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135
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When discussing error correction, what are the objects in the expression $PE_i^\dagger E_j P=\alpha_{ij} P$?
I've started reading the book "Quantum Computation and Quantum Information" by Michael A. Nielsen and Issac L. Chuang, specifically chapter 10 (about quantum error correction), and I'm ...
- 51
1
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1
answer
291
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What is meant by a "projection operator" in the book "Quantum Computation and Quantum Information"?
I've started reading the book "Quantum Computation and Quantum Information" by Michael A. Nielsen and Issac L. Chuang, specifically chapter 10 (about quantum error correction), and I'm ...
- 51
2
votes
1
answer
94
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How to compute the measurement probabilities of $|\phi\rangle=\sum_k c_k |k\rangle$ in a rotated basis $V|k\rangle$?
I came across the following question and have some conceptual questions.
Consider a general quantum state $|\phi\rangle$ of dimension $N$ spanned by some standard basis $\{|k\rangle,k=0,1,...N-1\}$. ...
- 123
1
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1
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237
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If density matrices are linear operators, what vectors do they operate on?
1. On page 73 of John Watrous' famous book, a quantum channel is defined as a linear map
$$\Phi: L(\mathcal{X})\rightarrow L(\mathcal{Y})$$
Now $L(\mathcal{X})$ stands for $L(\mathcal{X},\mathcal{X})$...
- 253
2
votes
1
answer
68
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What is the best notation to write pairs of one-qubit ket states?
I am working on coming up with practice problems for a QC course. I have a problem that considers two qubits as so:
$$|\psi_a\rangle = \alpha_a |0\rangle + \beta_a |1\rangle$$
$$|\psi_b\rangle = \...
- 165
1
vote
2
answers
461
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Can Dirac notation be used with 2 or more gates?
Can Dirac notation be used with 2 or more gates?
I've been trying to do the math with the $X$ and $Z$ ($X\otimes Z$) gates but I'm not getting the answer I should. In fact, the answer makes no sense.
...
- 45
2
votes
3
answers
250
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Is there any difference between "value of a qubit" and its "state"?
Value of a qubit and its state - is there any difference between these two terms in sense of terminology?
For example, can we name this state of a qubit also a value of a qubit:
$$
|\psi\rangle = \...
- 101
3
votes
1
answer
68
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Shouldn't the input state of Deutsh-Jozsa's algorithm look like $|0\rangle^{\otimes n}\otimes |1\rangle$ rather than $|0\rangle^{\otimes n}|1\rangle$?
According to this wikipedia page the initial state in Deutsch–Jozsa algorithm is written as follows:
$$|0\rangle^{\otimes n} |1\rangle$$
shouldn't it look like this?:
$$|0\rangle^{\otimes n} \otimes |...
- 33
4
votes
2
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669
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If the eigenvalues of $Z$ are $\pm1$, why are the computational basis states labeled with "$0$" and "$1$"?
The computational basis is also known as the $Z$-basis as the kets $|0\rangle,|1\rangle$ are chosen as the eigenstates of the Pauli gate
\begin{equation}
Z=\begin{pmatrix}1 & 0 \\ 0 & -1\end{...
- 133