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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8
votes
2answers
155 views

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 ...
3
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1answer
41 views

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 $...
3
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0answers
22 views

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 \\ \...
8
votes
1answer
176 views

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) ...
6
votes
1answer
94 views

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,...
2
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0answers
43 views

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 ...
5
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1answer
98 views

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] + ...
3
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1answer
55 views

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)~~~...
5
votes
1answer
96 views

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_{...
5
votes
0answers
102 views

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 ...