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More explicitly, this is the quantity | |, with the maximization performed with respect to all possible POVMs {}. To see why this is the case, we start observing that there is a unique decomposition ρ − σ = P − Q {\displaystyle \rho -\sigma =P-Q} with P , Q ≥ 0 {\displaystyle P,Q\geq 0} positive semidefinite matrices with ...
Fidelity is symmetric in its arguments, i.e. F (ρ,σ) = F (σ,ρ). Note that this is not obvious from the original definition. F (ρ,σ) lies in [0,1], by the Cauchy–Schwarz inequality. F (ρ,σ) = 1 if and only if ρ = σ, since Ψ ρ = Ψ σ implies ρ = σ. So we can see that fidelity behaves almost like a metric.
The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by the Boltzmann constant).
There are also nonintrusive model reduction methods that learn reduced models from data without requiring knowledge about the governing equations and internals of the full, high-fidelity model. Nonintrusive methods learn a low-dimensional approximation space or manifold and the reduced operators that represent the reduced dynamics from data.
However, the limitation is that the low-fidelity data may not be useful for predicting real-world expert (i.e., high-fidelity) performance due to differences between the low-fidelity simulation platform and the real-world context, or between novice and expert performance (e.g., due to training). [8] [9]
The Cirac-Zoller CNOT gate was not experimentally demonstrated with two ions until 8 years later, in 2003, with a fidelity of 70-80%. [5] Around 1998, there was a collective effort to develop two-qubit gates independent of the motional state of individual ions, [ 6 ] [ 1 ] [ 7 ] one of which was the scheme proposed by Klaus Mølmer and Anders ...
Fidelity is therefore a measure of the realism of a model or simulation. [4] Simulation fidelity has also been described in the past as "degree of similarity". [5] In quantum mechanics and optics, [6] the fidelity of a field is calculated as an overlap integral of the field of interest with a reference or target field.
Consider the real line with its usual Borel topology. Let denote the Dirac measure, a unit mass at the point in .The collection := {|} is not tight, since the compact subsets of are precisely the closed and bounded subsets, and any such set, since it is bounded, has -measure zero for large enough .