The Fubini-Study metric is the standard unitary-invariant Kähler metric on Complex projective space, induced from the unit sphere by the Hopf fibration. Its associated Kähler form is the Fubini-Study form; scaling conventions determine the area of a projective line.
The Fubini–Study metric is a Riemannian metric defined on complex projective space, specifically on the projective Hilbert space \( \mathbb{CP}^n \). It is often used in the context of quantum mechanics and quantum information theory as it provides a way to measure distances and angles between quantum states represented as rays in complex projective space.
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