Questions tagged [quantum-metrology]
The study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, particularly exploiting quantum entanglement and quantum squeezing.
28 questions
4
votes
1
answer
52
views
Why $\delta X = \frac{X_\textrm{est}}{|d\langle X_{\textrm{est}} \rangle_X/dX|}-X$ quantifies the derivation of a parameter estimation?
In a famous paper "Statistical Distance and the Geometry of Quantum States" by Braunstein and Caves, the authors discuss the problem of estimating an unknown parameter $X$. One considers an ...
- 143
1
vote
0
answers
80
views
Computing the QFI for a general Gaussian state
I found somewhere the following formula for the quantum Fisher information of a multimode Gaussian state $(\mathbf d_\theta, \sigma_\theta)$:
$$\tag{1}
H(\theta) = \frac{1}{2} \text{Tr}\left[ \left( \...
4
votes
3
answers
154
views
How to compute the energy of a non-eigenstate in a Heisenberg limited form?
Let us have a Hamiltonian $H$ and a state $|\psi\rangle = \sum_i a_i |E_i\rangle$, a linear combination of eigenstates $|E_i\rangle$ of $H$ with eigenvalues $E_i$. What is the best way to achieve a ...
- 603
0
votes
0
answers
30
views
Good resources for learning about quantum batteries and quantum metrology
I am a 1st year PhD student, beginning my research on quantum information. I would like to learn about quantum metrology and quantum batteries in depth, from scratch. Can anyone suggest good books/...
- 443
6
votes
1
answer
208
views
Where does the "error propagation formula" $(\Delta \theta)^2=(\Delta M)^2/|\partial_\theta\langle M\rangle|^2$ come from, in estimation theory?
Consider the single parameter estimation setting, where we have a distribution depending on $\theta$ and we're looking for a "good" estimator for $\theta$.
A commonly mentioned strategy, ...
glS♦
- 27.7k
4
votes
2
answers
182
views
Generalizing error propagation formula to multi-parameters
For single parameter phase estimation we have the Cramer-Rao bound $$(\Delta \theta)^2 \geq \frac{1}{F_{Q}[\rho, \hat{A}]},$$where $F_{Q}$ is the quantum Fisher information and where instead of an ...
- 941
3
votes
1
answer
77
views
Fisher information from likelihood function for discrete quantum case
In the context of a single phase estimation problem of a quantum photonics experiment. For example consider a 3-photon quantum circuit (such as the Mach-Zehnder which depends on some phase shift ...
- 941
0
votes
0
answers
42
views
Calculation of QCRB from QCRB
On page 3 of Zhuang et al. (2018), they found the quantum Cramér-Rao bound (QCRB) of the parameter using the quantum fisher information matrix. See Equations $(15)$ and Eq $(16)$.
The problem is ...
6
votes
1
answer
145
views
How to compute the SLDs for pure single-qubit states?
In Demkowicz-Dobrzanski et al. (arXiv:2001.11742), the authors mention in Eq. (74), page 22, that the symmetric logarithmic derivatives (SLDs) for pure states parametrised in the usual way via the ...
glS♦
- 27.7k
2
votes
0
answers
47
views
Fisher information of parametric channel
Suppose $\Phi_\theta$ is a quantum channel whose action can be written for any state $\rho\in \mathcal S(\mathcal H_S)$ in the Stinespring representation as $\Phi_\theta(\rho)= \text{Tr}_E(U_\theta (\...
- 39
3
votes
1
answer
382
views
How to compute the QFI of a thermal state?
Let $\rho=\frac{1}{Z}\exp(-\beta H)$ be the thermal state associated to the Hamiltonian $$H=\hbar\omega\sum_i\left( a_i^\dagger a_i+\frac12\right).$$
I wonder how the quantum Fisher information of ...
- 127
1
vote
0
answers
80
views
What are the similarity and difference between quantum fidelity estimation and parameter estimation problem?
Quantum fidelity (1) estimation is to estimate the similarity between two quantum states or process. Could quantum fidelity be viewd as a parameter? And what are the similarity and difference between ...
- 599
2
votes
0
answers
101
views
In quantum metrology, how do we achieve unbiased estimator in the local unbiased formalism?
In quantum metrology, the main goal is to estimate some unknown parameter to the limit of quantum mechanics. Suppose there's a unitary quantum channel $U_{\theta}=e^{-i\theta \sigma _z}$ with $\theta$ ...
- 3,179
4
votes
1
answer
65
views
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 \...
- 155
1
vote
1
answer
140
views
Prove that the Bures metric satisfies a contractive property and has unitary invariance
In this paper, the authors assert that the Bures metric satisfies a contractive property and has unitary invariance. These terms aren't defined or proved in the paper, nor is any reference given for a ...
- 831