Symbol hatθ
hatθ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
Quantum Fisher information measures the local statistical distinguishability of neighboring states. Braunstein and Caves derived the quantum statistical metric by optimizing distinguishability over measurements [ 9 ] . For a single parameter and independent repetitions, the quantum Cramér–Rao relation is commonly written . under the relevant regularity and unbiasedness conditions. The variance has squared-coordinate units, so has inverse-squared-coordinate units. Paris’s review emphasizes that quantum estimation is an optimization problem over measurements and explains the symmetric-logarithmic-derivative construction used to calculate the bound [ 10 ] .
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Symbol nu
nu occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol F_Q
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol θ
θ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Denominator: nu F_Q(θ)
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction.
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Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 68 · Evolutionary Physics
A Reference Frame Becomes Classical by Publishing Its Orientation
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.
Quantum Fisher information measures the local statistical distinguishability of neighboring states. Braunstein and Caves derived the quantum statistical metric by optimizing distinguishability over measurements [ 9 ] . For a single parameter and independent repetitions, the quantum Cramér–Rao relation is commonly written . under the relevant regularity and unbiasedness conditions. The variance has squared-coordinate units, so has inverse-squared-coordinate units. Paris’s review emphasizes that quantum estimation is an optimization problem over measurements and explains the symmetric-logarithmic-derivative construction used to calculate the bound [ 10 ] .
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