# Linked Questions

17 questions linked to/from How does bra-ket notation work?
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### 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 ...
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### 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 ...
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3 votes
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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. $\left<01\... 1 vote 2 answers 448 views ### Can Dirac notation be used with 2 or more gates? Can Dirac notation be used with 2 or more gates? I've been trying to do the math with the$X$and$Z$($X\otimes Z$) gates but I'm not getting the answer I should. In fact, the answer makes no sense. ... • 45 0 votes 2 answers 523 views ### 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 ... • 173 0 votes 3 answers 387 views ### 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,$|\psi^*\rangle \rightarrow |\psi\rangle$• 535 1 vote 1 answer 126 views ### 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 ... • 219 -1 votes 1 answer 144 views ### 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 &... 4 votes 1 answer 5k views ### How are the Pauli$X$and$Z$matrices expressed in bra-ket notation? [duplicate] For example: $$\rm{X=\sigma_x=NOT=|0\rangle\langle 1|+|1\rangle\langle 0|=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}}$$ $$\rm{Z=\sigma_Z=signflip=|0\rangle\langle 0|-|1\rangle\langle 1|=\... • 183 1 vote 1 answer 459 views ### Magnitudes and phases of coefficients of a qubit [duplicate] Quantum mechanics is based on the idea of waves, and waves have both a magnitude and a phase?$$|\psi\rangle = i\alpha|0\rangle + \beta|1\rangle.$$Does \alpha and \beta represent magnitude and i... • 313 5 votes 1 answer 245 views ### Where is the factor of -i in rotation gates coming from? As I understand it the Pauli-X, Y and Z gates are the same as their rotational gates with a rotation of \pi. But given the expression for those gates, I find that there is a factor of -i in each ... • 53 1 vote 1 answer 108 views ### How to write the map \mathbb C\ni z\mapsto zv in bra-ket notation? As part of a course, I've been asked to write a map C\rightarrow H,z \rightarrow zv for v \in H=C^3\otimes C^2, v=[1, 0, 0, 1, 0, 1] in bra-ket notation. However, I never written such a map ... 3 votes 1 answer 306 views ### How to read Dirac notation (without algebra)? I have no idea how to read Dirac notation.$$\left|↑↑ \right\rangle \tag{1}\left|↑↓\right\rangle+\left|↓↑\right\rangle \tag{2}\left|↑↓\right\rangle-\left|↓↑\right\rangle \tag{3}\left|↓... • 79 1 vote 1 answer 945 views ### 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 ... • 818 6 votes 2 answers 1k views ### 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 \...

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