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Quantum state tomography is a process by which, given a set of data representing the results of quantum measurements, a quantum state consistent with those measurement results is computed. [50] It is named by analogy with tomography , the reconstruction of three-dimensional images from slices taken through them, as in a CT scan .
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.
More explicitly, this is the quantity | |, with the maximization performed with respect to all possible POVMs {}. To understand why this maximum equals the trace distance between the states, note 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 ...
Vinyl microgroove phonograph records typically yield 55-65 dB, though the first play of the higher-fidelity outer rings can achieve a dynamic range of 70 dB. [25] German magnetic tape in 1941 was reported to have had a dynamic range of 60 dB, [26] though modern-day restoration experts of such tapes note 45-50 dB as the observed dynamic range. [27]
Besides describing lasers, coherent states also behave in a convenient manner when describing the quantum action of beam splitters: two coherent-state input beams will simply convert to two coherent-state beams at the output with new amplitudes given by classical electromagnetic wave formulas; [11] such a simple behaviour does not occur for ...
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.
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]
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.