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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.

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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_{...
Ghost-of-PPPF's user avatar
4 votes
1 answer
114 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's user avatar
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1 vote
1 answer
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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 ...
SescoMath's user avatar
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5 votes
1 answer
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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's user avatar
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11 votes
2 answers
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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's user avatar
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4 votes
2 answers
474 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 ...
Steven Sagona's user avatar
11 votes
0 answers
203 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, ...
Paul B. Slater's user avatar