1 vote
1k views

### 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?
• 439
1 vote
311 views

### 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 ...
• 577
6k views

• 143
1 vote
2k views

### 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 ...
252 views

### 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 ...
• 173
285 views

### 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? ...
• 21
1 vote
483 views

### 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 $i$...
• 313
252 views

### 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 ...
• 53
159 views

### 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 ...
• 183
156 views

### 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 ...
• 577
168 views

### 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 ...
• 21
138 views

### 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 ...
101 views

### 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 ...
• 145
1 vote
72 views

### 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 ...

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