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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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 ...
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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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Error in the Toth's 2012 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 ...
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