# 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.

25 questions
Filter by
Sorted by
Tagged with
1 vote
36 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 ...
60 views

115 views

### 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,...
1 vote
82 views

261 views

### 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) ...
766 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,...
96 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 ...
294 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_{...