Fidelitypreserving

Fidelitypreserving describes a property of a process, transformation, or protocol that keeps the fidelity between an input and its output within a prescribed bound, or exactly intact. Fidelity is a quantitative measure of how similar two objects are, which may be states, signals, or probability distributions. The exact definition of fidelity depends on the domain: in classical settings it often relates to the similarity of probability distributions, while in quantum information it is commonly defined as F(ρ, σ) = (Tr sqrt(sqrt(ρ) σ sqrt(ρ)))^2 for quantum states ρ and σ.

In practice, fidelitypreserving means that the transformation does not appreciably degrade the information content or representational accuracy of the original input. In data processing, a fidelity-preserving operation would reproduce the input faithfully, typically within a specified tolerance. Lossless data compression, for example, is fidelity-preserving because the original data can be recovered exactly. In communications and archiving, fidelity-preserving methods aim to minimize distortion during transmission or storage.

In quantum information science, certain transformations are inherently fidelity-preserving. Unitary operations are fidelity-preserving for all state pairs, since they preserve inner products and, hence, distinguishability. More generally, isometric mappings preserve fidelity. By contrast, many noisy or lossy channels do not guarantee fidelity preservation, and fidelity can degrade depending on the noise model and the states involved.

Fidelitypreserving contrasts with lossy processes, where some information or accuracy is intentionally sacrificed. It remains a central concept in fields such as signal processing, data compression, and quantum computing when ensuring accurate representation and reconstruction are important. See also fidelity, isometry, lossless compression, and quantum channels.