Questions tagged [metrics]
A metric is a generalization of the concept of "distance" in the Euclidean sense. Metric spaces are sets on which a metric is defined, and arise as a special case of the more general notion of a topological space.
7
questions
1
vote
0
answers
53
views
example of a Schur-concave metric on density matrices
I am looking for an example of a metric/distance function $D(\rho,\sigma)$ which is Schur-concave apart from fidelity. In particular I am interested in the relation
$D(\rho, \sum_i p_i \sigma_i) \leq_{...
- 151
3
votes
1
answer
63
views
How to go from finite to infinitesimal form of the Fubini-Study metric?
As mentioned e.g. in the Wikipedia page, given a pair of pure states $\psi,\phi\in\mathbb{CP}^{N-1}$, the geodesic distance between them is
$$\gamma(\psi,\phi) = \arccos\sqrt{\frac{\langle\psi|\phi\...
glS♦
- 23k
1
vote
1
answer
70
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 ...
- 485
5
votes
1
answer
721
views
What is the connection between Bures metric and (finite) Bures distance?
The Wikipedia page discussing the Bures metric introduces it as the Hermitian 1-form operator $G$ defined implicitly by $\rho G+G\rho = \mathrm d\rho$, and which induces the corresponding Bures ...
glS♦
- 23k
10
votes
2
answers
738
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 ...
glS♦
- 23k
4
votes
2
answers
398
views
Is there a straightforward way to calculate the quantum volume for simple systems?
There are a few people who ask how to calculate IBM's "quantum volume", but it's not clear what the actual mathematical definition of this is. In the answers here, people just point to ...
- 1,089
11
votes
0
answers
195
views
Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities
For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
- 879