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Newest 'measurement' Questions - Quantum Computing Stack Exchange
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Learn more about TeamsQuestions tagged [measurement]
For questions related to measurement and its effects as relevant to quantum computation and quantum information.
765 questions
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2
votes
1
answer
64
views
How to transform the density matrix from one basis to another basis
Suppose I have a density matrix for 2 qubits which is 4 by 4, in $Z$ basis $\left(|0\rangle,|1\rangle\right)$. Now I want to transform the density matrix to $X$ basis $\left(|+\rangle,|-\rangle\right)$...
10
votes
1
answer
215
views
Is it hard to invert unitary effects implemented using feedback?
It's well know that if you have a circuit made up of only unitary operations, it's trivial to invert the circuit. Just reverse the order of operations, and invert each individual operation.
However, ...
1
vote
1
answer
56
views
Modeling readout errors for non-destructive measurements in Stim
I am currently trying to implement a QEC code in stim that is based on non-destructive measurements as core operations and want to add readout errors on these measurements as noise. For destructive ...
1
vote
0
answers
52
views
How to measure in practice the average of an observable?
Given a $n$ qubit quantum register in state $|\psi\rangle$, I have a basic question about assessing the average of an observable $\hat{O}$ with respect to state $|\psi\rangle$ :
\begin{equation}
\...
0
votes
1
answer
83
views
Shor code: arbitrary quantum error-correction
For describing Shor code for arbitrary error-correction, Nielsen and Chuang in page 434 say: we describe the noise by a trace-preserving quantum operation $\mathcal{E}$
$$\mathcal{E}(|\psi\rangle\...
0
votes
0
answers
45
views
Equivalence of projective measurement with general measurement
Nielsen and Chuang in page 91 say a very important thing: "projective measurements augmented by unitary operations turn out to be completely equivalent to general measurements, as shown in ...
0
votes
1
answer
106
views
Qiskit gives different statevectors when performing partial trace
I am building a circuit using Qiskit that contains many computational qubits and several ancilla qubits. Here is a toy example:
...
1
vote
0
answers
49
views
applying Haar random unitary to projection and pure states and compute its trace
I have this question when I read the proof of Theorem 4 in This paper. Here are the settings:
\begin{align}
&|\phi\rangle^{BC}: \text{The reduction of a pure state $|\phi\rangle^{ABCD}$ where A,C ...
0
votes
2
answers
68
views
Rotations that don’t change the outcomes probabilities in X and Z
Is there a rotation operator that doesn't change the outcome probability when measuring either on basis X or Z in the scenario where I only change the sign of the angle?
I was thinking of $R_y(\pm\...
2
votes
1
answer
187
views
Complexity of checking if a circuit is deterministic or not?
Suppose I am given a list of gates for some circuit. I start with some fixed state, say $\vert 000..\rangle$, and measure the output in the computational basis. I want to know if the circuit is ...
3
votes
1
answer
98
views
Hong Ou Mandel interference using Bell sates
In the standard Hong Ou Mandel interferometer, if identical photons are sent as input to a beam splitter, they will bunch at the output and so the rate of coincidences between the two outputs will ...
0
votes
2
answers
111
views
After applying CNOT, is it equivalent to measure the control or the target?
This is a follow up to What happens after applying CNOTs and measuring either register?
I have been playing with some problem that involves intermediate measurements after applying a CNOT. Here are ...
3
votes
2
answers
139
views
What happens after applying CNOTs and measuring either register?
Suppose I have a multi-qubit quantum state of the form:
$$
|\psi\rangle = \sum_i a_i |i\rangle |0^n\rangle |\phi_i\rangle\;,
$$
where $|\phi_i\rangle$ is some pure state (on a separate subsystem) that ...
3
votes
1
answer
402
views
Legal to take inner product between a two-qubit and single-qubit state?
Given a single-qubit state $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$, is it fine to calculate something like:
$$\langle\Phi^+|\psi\rangle = \frac{1}{\sqrt{2}}(\alpha\langle0| + \beta\langle1|),$$
...
2
votes
1
answer
114
views
Prove the relation between trace norm and fidelity for pure states
I encountered an exercise as follows:
Consider two generic pure states ( $|\Psi\rangle$, $|\Phi\rangle $).
Prove the following exact relation between the fidelity and the trace
distance:
$$\frac{1}{2}...
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Related Tags
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povm × 54
error-correction × 52
programming × 48
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linear-algebra × 38
probability × 35
nielsen-and-chuang × 35
bell-basis × 33
quantum-circuit × 30
density-matrix × 30
quantum-algorithms × 28
circuit-construction × 28
ibm-q-experience × 28
projection-operator × 27
pauli-gates × 24
information-theory × 23
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simulation × 20
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