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The fidelity between two quantum states and , expressed as density matrices, is commonly defined as: [1] [2] (,) = ().The square roots in this expression are well-defined because both and are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem.
One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.
This leads to a constraint that α 2 + β 2 = 1; more generally the sum of the squared moduli of the probability amplitudes of all the possible states is equal to one. If to understand "all the possible states" as an orthonormal basis , that makes sense in the discrete case, then this condition is the same as the norm-1 condition explained above .
Investment giant Fidelity believes its shares of X, the platform formerly known as Twitter, are worth 71.5% less than when Musk first purchased the social media company in October 2022, according ...
The mutual fund giant — and X investor — estimates that the social media platform is worth 71.5% less than the $44 billion Musk bought it for in 2022. Fidelity again downgrades estimated ...
Peak signal-to-noise ratio (PSNR) is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed as a logarithmic quantity using the decibel scale.
The new valuation from Fidelity implies that it believes X is now worth just $9.4 billion — a far cry from the $44 billion that Musk paid. Other investors could value X differently.
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]