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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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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 ...
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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 ...
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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 ...
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1 vote
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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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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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1 vote
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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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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_{...