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Newest 'quantum-fisher-information' Questions - Quantum Computing Stack Exchange
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Learn more about TeamsQuestions tagged [quantum-fisher-information]
The quantum analog of the classical Fisher information, a way of measuring the amount of information that a random observable A carries about an unknown parameter θ of a distribution that models A. The quantum Fisher information constrains the achievable precision in the statistical estimation of θ via the quantum Cramér–Rao bound.
34 questions
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1
vote
0
answers
85
views
Computing the QFI for a general Gaussian state
I found somewhere the following formula for the quantum Fisher information of a multimode Gaussian state $(\mathbf d_\theta, \sigma_\theta)$:
$$\tag{1}
H(\theta) = \frac{1}{2} \text{Tr}\left[ \left( \...
1
vote
0
answers
69
views
Help to understand a QFI derivation
Can anyone help me understand the QFI derivation being done in Appendix C of this paper?
The density matrix $\rho = \frac12(|\psi_1\rangle\langle\psi_1|+|\psi_2\rangle\langle\psi_2|)$. I understand ...
4
votes
0
answers
65
views
How to derive the higher terms in the Taylor expansion of the Bures fidelity?
The Wikipedia article for the quantum Fisher Information mentions that one can expand the Bures fidelity and the quantum Fisher Information will appear as the second-order correction term.
However in ...
4
votes
2
answers
188
views
Generalizing error propagation formula to multi-parameters
For single parameter phase estimation we have the Cramer-Rao bound $$(\Delta \theta)^2 \geq \frac{1}{F_{Q}[\rho, \hat{A}]},$$where $F_{Q}$ is the quantum Fisher information and where instead of an ...
3
votes
1
answer
69
views
In what limit does the estimator sample variance converge to the Cramer-Rao bound?
In the context of a single phase estimation problem of a quantum photonics experiment (related post). For example consider a 3-photon quantum circuit (such as the Mach-Zehnder which depends on some ...
2
votes
0
answers
81
views
Modelling Mach-Zehnder and saturating Cramer-Rao bound
I am simulating (using Mathematica) a Mach-Zehnder interferometer, with photon counting measurements at the end (based on the setup described in the recent post) for the input state $|\psi\rangle:=|0,...
3
votes
1
answer
78
views
Fisher information from likelihood function for discrete quantum case
In the context of a single phase estimation problem of a quantum photonics experiment. For example consider a 3-photon quantum circuit (such as the Mach-Zehnder which depends on some phase shift ...
0
votes
0
answers
43
views
Calculation of QCRB from QCRB
On page 3 of Zhuang et al. (2018), they found the quantum Cramér-Rao bound (QCRB) of the parameter using the quantum fisher information matrix. See Equations $(15)$ and Eq $(16)$.
The problem is ...
6
votes
1
answer
147
views
How to compute the SLDs for pure single-qubit states?
In Demkowicz-Dobrzanski et al. (arXiv:2001.11742), the authors mention in Eq. (74), page 22, that the symmetric logarithmic derivatives (SLDs) for pure states parametrised in the usual way via the ...
2
votes
0
answers
49
views
Fisher information of parametric channel
Suppose $\Phi_\theta$ is a quantum channel whose action can be written for any state $\rho\in \mathcal S(\mathcal H_S)$ in the Stinespring representation as $\Phi_\theta(\rho)= \text{Tr}_E(U_\theta (\...
1
vote
0
answers
66
views
Classical Fisher Information for 1-qubit vs 2-qubit in PennyLane
I'm attempting to examine the Classical Fisher Information (CFI) for a 1-qubit system in comparison to a 2-qubit system.(PennyLane)
I anticipated that the CFI for the 2-qubit system would be double(at ...
2
votes
0
answers
147
views
Plotting Fisher Information using PennyLane
I made 2-qubit based circuit with post-selection method.
Post-selection method is, Let
$$
K = \begin{bmatrix}
\sqrt{1-\gamma} & 0 \\
0 & 1
\end{bmatrix}\,.
$$
Then,
$$ \rho_{\text{post-...
3
votes
1
answer
391
views
How to compute the QFI of a thermal state?
Let $\rho=\frac{1}{Z}\exp(-\beta H)$ be the thermal state associated to the Hamiltonian $$H=\hbar\omega\sum_i\left( a_i^\dagger a_i+\frac12\right).$$
I wonder how the quantum Fisher information of ...
2
votes
1
answer
276
views
Quantum computation of classical Fisher information
Consider a pure $n$-qubit quantum state $|\psi_\theta\rangle$ prepared by some parametrized quantum circuit. There exist well-known algorithms to efficiently estimate the quantum Fisher information ...
1
vote
1
answer
348
views
Create qnode with density matrix on pennylane
I'm using pennylane.
What I want to do is
Create a qnode with the 2*2 density matrix of a single qubit one. It has the parameter as phi
Given density matrix:
$$\...
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