QuantenzustandsVerhältnis

QuantenzustandsVerhältnis is a coined term used to describe the relation between components of a quantum state in a given basis. It denotes how the amplitudes or populations of different basis states compare to each other, including both their magnitudes and relative phases. It is not a standard, universally defined quantity in formal quantum mechanics, but a convenient label for discussing state structure in interferometric and control contexts.

Mathematically, for a state |ψ> expressed in a basis {|i⟩} as |ψ⟩ = ∑i ci|i⟩, the QuantenzustandsVerhältnis can be represented by the set of ratios ri = ci / cref relative to a reference coefficient cref, or by the amplitude ratio in a two-state system via r = c1 / c2. The corresponding population ratio is R = |c1|^2 / |c2|^2. The relative phase between components is also part of the concept, since complex amplitudes carry phase information that influences interference.

Interpretation and use: the QuantenzustandsVerhältnis encodes how much weight is given to each basis component and how their phases align. It directly affects measurement statistics in the chosen basis and the visibility of interference fringes. Because the quantities are basis-dependent, they provide useful but non-general summaries of a state’s structure in specific experimental contexts.

Measurement and estimation: in practice, the ratios are inferred from quantum state tomography or from measured probabilities and known projective measurements. The concept helps in discussing state preparation, gate operations, and coherence without committing to a single invariant quantity.

Relation to other concepts: it differs from fidelity or state overlap, which are basis-independent, and it complements descriptions based on amplitudes, phases, and density matrices.