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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.
The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 1996 by the theoretical physicist David P. DiVincenzo, [1] as being those necessary to construct such a computer—a computer first proposed by mathematician Yuri Manin, in 1980, [2] and physicist Richard Feynman, in 1982 [3] —as a means to efficiently simulate quantum systems, such ...
Relating to the team's nationality because of teams' bases in Britain several mistakes occurred on official entry lists issued by or podium ceremonies organized by the FIA or race organisers, e.g. Wolf [31] [32] holding the Canadian nationality and Shadow (in 1973) [33] and Penske [34] [35] both holding the American nationality all identified ...
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.
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 ...
Wave functions represent quantum states, particularly when they are functions of position or of momentum. Historically, definitions of quantum states used wavefunctions before the more formal methods were developed. [4]: 268 The wave function is a complex-valued function of any complete set of commuting or compatible degrees of freedom.
Values of the IPR close to 1 correspond to localized states (pure states in the analogy), as can be seen with the perfectly localized state () =,, where the IPR yields | | =. In one dimension IPR is directly proportional to the inverse of the localization length, i.e., the size of the region over which a state is localized.
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.