the Fubini–Study metric (IPA: /fubini-ʃtuːdi/) is a Kähler metric on a complex projective space CPn endowed with a Hermitian form. This metric was originally...

Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric. Born in Venice, he...

Hilbert space, it becomes the Fubini–Study metric; when written in terms of mixed states, it is the quantum Bures metric. Considered purely as a matrix...

Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone. The Bures metric may be defined as [...

Fubini a year before. The distance Study refers to is a Hermitian form on complex projective space. Since then this metric has been called the Fubini–Study...

Hermitian metric is closed for dimensional reasons. There is a standard choice of Kähler metric on complex projective space CPn, the Fubini–Study metric. One...

-sphere, hyperbolic space, and complex projective space with the Fubini-Study metric. A Riemannian manifold is said to have constant curvature κ if every...

then the visualization is less useful. The natural metric on the Bloch sphere is the Fubini–Study metric. The mapping from the unit 3-sphere in the two-dimensional...

} Up to a constant factor, this metric agrees with the standard Fubini–Study metric on complex projective space (of which the Riemann...

information-geometric optimization algorithms. Its quantum version is Fubini-study metric. Relative entropy satisfies a generalized Pythagorean theorem for...

fibration. Complex projective space carries a (Kähler) metric, called the Fubini–Study metric, in terms of which it is a Hermitian symmetric space of...

Inner angle may refer to: internal angle of a polygon Fubini–Study metric on a Hilbert space This disambiguation page lists mathematics articles associated...

counterexample is complex projective space with the Fubini–Study metric; sectional curvatures of this metric take on values between 1 and 4, with endpoints...

projective space. Because projective space carries a Kähler metric, the Fubini–Study metric, such a manifold is always a Kähler manifold. By Chow's theorem...

natural Fubini–Study metric on a projective space which one can restrict to the algebraic variety. By definition, if ω is the Kähler metric on the algebraic...

projective space or projective Hilbert space, geometrized with the Fubini–Study metric, the theory of quantum mechanics and more generally quantum field...

time-varying Hamiltonians. In this case, the Bures metric must be employed in place of the Fubini–Study metric. A mixed state can be understood as a sum over...

{CP} ^{n}} , with the Fubini–Study metric, have k = 2 n + 2. {\displaystyle k=2n+2.} Calabi–Yau manifolds admit an Einstein metric that is also Kähler,...

1969. Eugene was born in Turin, Italy to Guido Fubini, known for Fubini's theorem and the Fubini–Study metric. He graduated from the Technical Institute of...

obeys the triangle inequality, so this angle is a metric on the state space: the Fubini–Study metric. R. Jozsa, Fidelity for Mixed Quantum States, J. Mod...

the space in terms of its systole. It is known that the Fubini–Study metric is the natural metric for the geometrisation of quantum mechanics. In an intriguing...

(H_{n})=\mathbb {C} \mathbf {P} ^{n-1}} , which carries a Kähler metric, called the Fubini–Study metric, derived from the Hilbert space's norm. As such, the projectivization...

{\displaystyle \mathbb {HP} ^{n}} carries a natural Riemannian metric analogous to the Fubini-Study metric on C P n {\displaystyle \mathbb {CP} ^{n}} , with respect...

Ricci tensors is given in the n=2 subsection of the article on the Fubini-Study metric. Circular points at infinity del Pezzo surface Toric geometry Fake...

distance metric given by the Fubini–Study metric. To recap, the quantum probability of a language being accepted can be interpreted as a metric, with the...

curvature and parallel Ricci tensor (such as the flat torus or the Fubini–Study metric on complex projective space). Such matrix inequalities are sometimes...

complex projective space, which has a metric of nonnegative curvature operator (the Fubini-Study metric) but no metric of constant curvature, makes it unclear...

mapping to the Riemann sphere. The standard metric on the unit sphere agrees with the Fubini–Study metric on the Riemann sphere. The set of all lines...

after restricting the standard Hermitian metric on C n {\displaystyle \mathbb {C} ^{n}} or the Fubini-Study metric on C P n {\displaystyle \mathbb {CP} ^{n}}...

soliton in non-linear sigma models Polyakov action WZW model Fubini–Study metric, a metric often used with non-linear sigma models Ricci flow Scale invariance...