Linked Questions

2 votes
2 answers

What does the phase $\phi_1$ in a state $|\psi\rangle=a_1|0\rangle+a_2|1\rangle$ with $a_j=r_j e^{i\phi_j}$ say about state $|1\rangle$?

I'm a beginner in quantum computing and this question has been bugging me for quite some time. I have seen in various articles that a qubit is a device whose state can be represented by a unit vector ...
Adeeb HS's user avatar
3 votes
2 answers

Optimising state tomography for fully entangled states

As tomography methods are usually inefficient, it's interesting to find good approximation. I was wondering the following: Assume one wants to estimate a state $\rho$ on $n$-qubits. Given a basis of ...
Daniele Cuomo's user avatar
3 votes
2 answers

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\...
Michael Kročka's user avatar
1 vote
2 answers

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. ...
Doug's user avatar
  • 45
0 votes
2 answers

How do I apply a matrix to a ket state?

If we have the following matrix: $$\frac{1}{\sqrt{2}}\begin{pmatrix}1&1&0&0\\ 1&-1&0&0\\ 0&0&1&-1\\ 0&0&1&1\end{pmatrix}$$ How do we find the output for ...
Xavi's user avatar
  • 173
0 votes
3 answers

How to prove that the transpose operation maps an arbitrary qubit to its complex conjugate?

How to prove that the transpose operation maps an arbitrary qubit to its complex conjugate, $|\psi^*\rangle \rightarrow |\psi\rangle$
heromano's user avatar
  • 535
1 vote
1 answer

What is the difference between the states $i|1\rangle$ and $|+i\rangle$?

I am new to Quantum computing. I see $|\mbox{+}i\rangle$ state maps to y-axis on bloch sphere ($\theta = 90$ degree and $\phi = 90$ degree) while $i|1\rangle$ maps on x-axis, $i|1\rangle$ is stated as ...
Kumar's user avatar
  • 219
-1 votes
1 answer

Outer Product Intution [duplicate]

Please, help me understand this statement. The outer product notation for matrices also gives an intuitive input-output relation for them. For instance, the matrix |0⟩ ⟨1| + |1⟩ ⟨0| can be read as &...
Binshumesh sachan's user avatar
4 votes
1 answer

How are the Pauli $X$ and $Z$ matrices expressed in bra-ket notation? [duplicate]

For example: $$\rm{X=\sigma_x=NOT=|0\rangle\langle 1|+|1\rangle\langle 0|=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}}$$ $$\rm{Z=\sigma_Z=signflip=|0\rangle\langle 0|-|1\rangle\langle 1|=\...
John T's user avatar
  • 183
1 vote
1 answer

Magnitudes and phases of coefficients of a qubit [duplicate]

Quantum mechanics is based on the idea of waves, and waves have both a magnitude and a phase? $$|\psi\rangle = i\alpha|0\rangle + \beta|1\rangle.$$ Does $\alpha$ and $\beta$ represent magnitude and $i$...
guest's user avatar
  • 313
5 votes
1 answer

Where is the factor of $-i$ in rotation gates coming from?

As I understand it the Pauli-X, Y and Z gates are the same as their rotational gates with a rotation of $\pi$. But given the expression for those gates, I find that there is a factor of $-i$ in each ...
Saxodrum's user avatar
1 vote
1 answer

How to write the map $\mathbb C\ni z\mapsto zv$ in bra-ket notation?

As part of a course, I've been asked to write a map $C\rightarrow H,z \rightarrow zv$ for $v \in H=C^3\otimes C^2$, $v=[1, 0, 0, 1, 0, 1]$ in bra-ket notation. However, I never written such a map ...
humourous_mug's user avatar
3 votes
1 answer

How to read Dirac notation (without algebra)?

I have no idea how to read Dirac notation. $$\left|↑↑ \right\rangle \tag{1}$$ $$\left|↑↓\right\rangle+\left|↓↑\right\rangle \tag{2}$$ $$\left|↑↓\right\rangle-\left|↓↑\right\rangle \tag{3}$$ $$\left|↓...
Logan's user avatar
  • 79
1 vote
1 answer

Measurement of a qubit and storage of the information on a bit

Suppose we have the quantum circuit below with a quantum register of 2 qubits and a classical register of 2 bits. The Hadamard gates and CNOT gate are not important for the question. When we measure a ...
Bidon's user avatar
  • 818
6 votes
2 answers

How to translate matrix back into Dirac notation?

In Circuit composition and entangled states section of Wikipedia's article on Quantum logic gates the final result of a combined Hadamard gate and identity gate on $|\Phi^{+}\rangle$ state is: $ M \...
Michał Zając's user avatar

15 30 50 per page