Linked Questions

1 vote
1 answer

What is meaning of 'up to a global phase'? [duplicate]

What is the importance of global phase? How it affect a unit vector if we see it on a Bloch sphere? What is the meaning of 'up to global phase' in exercise 4.3 of Nielsen and Chuang?
zircon's user avatar
  • 419
1 vote
1 answer

What is the significance of the phase angle? [duplicate]

I've the following circuit which gives an output of 1 with a phase angle of 3π/4. When we measure the circuit all we get is the ...
Van Peer's user avatar
  • 547
7 votes
2 answers

What is the square root of the NOT gate? [duplicate]

I have encountered different matrix of operator "the Square Root of NOT gate". For example, the matrix is specified here: $\sqrt {NOT} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} {1 + i}&...
alexhak's user avatar
  • 451
2 votes
5 answers

How to eliminate the global phase of a state vector?

Say that I have a qubit that began in the $|0\rangle$ state and then the Hadamard gate is applied, resulting in the following state: $ \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{...
bddicken's user avatar
  • 143
6 votes
1 answer

What happens with first phase factor in QFT?

I'm using Mermin's Quantum Computer Science book to understand Shor's algorithm, but I can't figure out why one of the phase factors drops out of the probability for measuring a certain y. This is ...
jvdh's user avatar
  • 163
1 vote
1 answer

How do two qubit states differing by a global phase relate to each other?

I have looked at the following: What is the difference between a relative phase and a global phase? In particular, what is a phase? Global and relative phases of kets in QM Global phases and ...
M. Al Jumaily's user avatar
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
2 votes
1 answer

What is the "quantum phase" of a quantum state?

On this page IMBQ docs, until the sentence '..and since the global phase of a quantum state is not detectable..' I follow everything. However 'quantum phase' is introduced without any explaination? ...
Tim's user avatar
  • 21
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
3 votes
1 answer

Are $(|00\rangle-|11\rangle)/\sqrt2$ and $(|11\rangle-|00\rangle)/\sqrt2$ the same quantum state?

The state $(|00\rangle-|11\rangle)/\sqrt2$ is an entangled state. If we think about the state $(|11\rangle-|00\rangle)/\sqrt2$, is this also entangled, but with maybe a phase change? The above two can ...
Kittu A's user avatar
  • 163
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
2 votes
3 answers

What is the difference between $|+\rangle$ and $|-\rangle$?

What is the difference between $|+\rangle$ and $|-\rangle$. I was reading about quantum states and found that $|+\rangle$ and $|-\rangle$ represent state in superposition of other states. I was just ...
Vinay Sharma's user avatar
0 votes
2 answers

Can the phase in a qubit be expressed as a phase on another qubit in a larger system?

$\newcommand{\ket}[1]{\left|#1\right>}$Consider two qubits, $\ket{1}$ and $e^{i \theta}\ket{\psi}$ (what the qubits are doesn't actually matter). We express these in a single system using their ...
tpws's user avatar
  • 88
3 votes
1 answer

Clarification defining/finding the relative phase of a qubit

Let the vector $ |V\rangle = r_0 e^{i\theta_0} |0\rangle + r_1 e^{i\theta_1} |1\rangle $ correspond to the state of a qubit where $r_0,r_1,\theta_0,\theta_1 \in \mathbb{R}$. According to p. 22 of ...
RyRy the Fly Guy's user avatar
1 vote
1 answer

Why does the point $(0,0,-1)$ on the bloch sphere correspond to the state $|1\rangle$ and not $-|1\rangle$ or $e^{i \phi}|1\rangle$?

In this representation for points on the $Z$-axis, $\phi$ is not defined. If the point $(0, 0, 1)$ is taken since $\theta$ is $0$ and $\sin(\theta/2)$ is zero, it doesn't matter what $\phi$ is. The ...
D Star Let's Explore's user avatar