Questions 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.
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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 ...
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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,
$$ \rho_{\text{post-...
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How to compute the QFI of a thermal state?
Let $\rho=\frac{1}{Z}\exp(-\beta H)$ be the thermal state associated to the Hamiltonian $$H=\hbar\omega\sum_i\left( a_i^\dagger a_i+\frac12\right).$$
I wonder how the quantum Fisher information of ...
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Quantum computation of classical Fisher information
Consider a pure $n$-qubit quantum state $|\psi_\theta\rangle$ prepared by some parametrized quantum circuit. There exist well-known algorithms to efficiently estimate the quantum Fisher information ...
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Create qnode with density matrix on pennylane
I'm using pennylane.
What I want to do is
Create a qnode with the 2*2 density matrix of a single qubit one. It has the parameter as phi
Given density matrix:
$$\...
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Problems trying to plot the classical Fisher information with Pennylane
I'm working with pennylane. My goal is to plot CFI(Classical Fisher Information)with following quantum state.
With the above equation I set gamma as 0. Then It becomes:
If gamma is not equal to zero,...
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How is the quantum geometric tensor derived?
In https://arxiv.org/abs/2302.13515 the authors discuss in page 23 the quantum geometric tensor, defined as
$$\mathcal Q_{\mu\nu} = \langle\partial_\mu\Psi|(I-|\Psi\rangle\!\langle\Psi|)|\partial_\nu\...
glS♦
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What is the classical Fisher information of a parametrized coherent state $|\alpha_\theta\rangle$?
Suppose $|\alpha_\theta\rangle$ is a coherent state depending on the real parameter $\theta$. What is the classical Fisher information it carries?
There are explicit formulae for the quantum Fisher ...
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What are the antisymmetric terms in $\sigma_{mn}$ in the expression for the Fisher information?
Given a parameter-dependent density operator $\hat\rho^\lambda$ and its spectral decomposition $\{\rho_m^\lambda, |\psi_n^\lambda\rangle\}$, Eq. $(17)$ from this review shows that one can compute its ...
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Why can't Quantum Fisher Information be negative?
Quantum Fisher Information is proportional to Fidelity susceptibility.
Mathematically the equation is:
$QFI=-\frac{\partial^2 d_B(\epsilon) }{\partial \epsilon^2}$
where above equation shows QFI is ...
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How do I find Quantum Fisher Information from an array of fidelity values for various parameter values?
I have an array of Fidelity values corresponding to parameter values.
For example,
eps=[0,0.1,0.2....,1]
where eps is the parameter
Fid=[1.0, 0.9, 0.96, 0.91, 0.85, 0.78, 0.71, 0.65, 0.59, 0.54]
I ...
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Paris 2009 paper on Quantum Estimation. From eq. 12 to eq. 16
In the paper "Quantum estimation for quantum technology", by Matteo Paris (2009), one is concerned with estimating a parameter $\lambda$ encoded in a quantum state $\rho_\lambda = \sum_n \...
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How to derive the quantum Fisher information from the relative entropy?
The quantum relative entropy (QRE) between two states $\rho$ and $\sigma$ is given by
$$
S(\rho\|\sigma)=\operatorname{Tr}(\rho\ln\rho)-\operatorname{Tr}(\rho\ln\sigma)
$$
Now if $\rho$ and $\sigma$ ...
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Is Quantum Cramer-Rao bound for single parameter always attainable?
First I will give some background of Quantum Cramer-Rao bound. There is an amount called Fisher Information:$F(\lambda)=\sum_x{p\left( x|\lambda \right) \left( \partial _{\lambda}\ln p\left( x|\lambda ...
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What does $\langle\partial_i\psi(\theta)|\psi(\theta)\rangle$ mean when implementing the Quantum Fisher information matrix?
Following this paper, the quantum Fisher information matrix (QFIM) - $\mathcal{F}$ can be calculated as:
$\mathcal{F}_{i, j}(\theta)=4 \operatorname{Re}\left[\left\langle\partial_{i} \psi(\boldsymbol{\...
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Does the symmetric logarithmic derivative operator have a geometric interpretation?
In the context of Bures metric and quantum Fisher information, an important object is the symmetric logarithmic derivative (SLD). This is usually introduced as a way to express the derivative of a ...
glS♦
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Unit vanishes in the Quantum Cramer-Rao Bound?
The Quantum Cramer-Rao Bound states that the precision we can achieve is bounded below by:
$$(\Delta \theta)^2\ge\frac{1}{mF_Q[\varrho,H]},$$
where $m$ is the number of independent repetitions, and $...
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How does the quantum Fisher information provide bounds for the estimation of output states?
Assume you have some quantum process $Q$ (e.g. quantum state tomography) that intakes initialised states $\rho_{i}$, $i=1,\ldots,n$ and gives some output $\rho'_i$.
$$
\rho_1 \to Q \to \rho'_1 \\
\...
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Understanding the $M$ upper bound in the paper: "Multipartite entanglement and high-precision metrology"
This paper is a paper in 2012 and cited by a lot of papers. And there does not exist comment in arxiv or error statement in PRA. But when I reading this paper, I think the right part of the eq(23) ...
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What is the difference between "Shot-Noise-Limit" and "Standard Quantum Limit"?
It seems that in a lot of papers in the field of quantum metrology, there are two terms Shot-Noise-Limit and Standard Quantum Limit which are frequently referred to. What's the difference between them,...
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What happens in the Cramer-Rao bound if the quantum Fisher information is zero?
The famous Cramer-Rao bound is $$\Delta\theta\ge\frac{1}{\sqrt {F[\rho,H]}}$$
But what happens if the denominator vanishes, i.e., $F[\rho,H]=0$ ($F[\rho,H]$ here stands for the quantum fisher ...
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How is the connection between Bures fidelity and quantum Fisher information derived?
I recently came to know that there is a connection between Bures Fidelity $(F_B)$ and Quantum Fisher Information $(F_Q)$ given by
$$[F_{B}(\rho, \rho_\theta)]^2 = 1 - \frac{\theta^2}{4} F_Q[\rho, A] + ...
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Stabilizer state QFI lower limit query
On page 1 of this paper it states that the QFI (Quantum Fisher Information) for pure states $\psi$ is $$\mathcal{Q}(\psi) = \sum_{i,j=1}^n\text{Tr}(X_iX_j\psi)-\text{Tr}(X_i \psi)\text{Tr}(X_j \psi)~~~...
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Why is the quantum Fisher information for pure states $F_Q[\rho,A]=4(\Delta A)^2$?
Assume that a density matrix is given in its eigenbasis as $$\rho = \sum_{k}\lambda_k |k \rangle \langle k|.$$ On page 19 of this paper, it states that the Quantum Fisher Information is given as $$F_{...
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Why is the quantum Fisher information $J_f=[f(\frac43-f)]^{-1}$ for maximally entangled qubit pairs?
I am reading paper Channel Identification and its Impact on Quantum LDPC Code Performance where the authors discuss the scenario where the decoder of a Quantum LDPC code uses an estimation of the ...
