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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.
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In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions.
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The approach is based on the relation between the fidelity and the quantum Fisher information and that the fidelity can be computed based on semidefinite programming. For systems in thermal equibirum, the quantum Fisher information can be obtained from the dynamic susceptibility.
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) [1] or Helstrom metric (named after Carl W. Helstrom) [2] defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the ...