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The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. [1][2][3][4][5] It is one of the central quantities used to qualify the utility of an input state, especially in Mach–Zehnder (or, equivalently, Ramsey) interferometer-based phase or parameter estimation ...
hide. In mathematical statistics, the Fisher information (sometimes simply called information[ 1 ]) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, [1][2][3] and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term.
The quantum Cramér–Rao bound is the quantum analogue of the classical Cramér–Rao bound. It bounds the achievable precision in parameter estimation with a quantum system: where is the number of independent repetitions, and is the quantum Fisher information. [1] [2]
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 Euclidean inner product from the ...
Bures metric. 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 ...
Quantum metrology is the study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, [1][2][3][4][5][6] particularly exploiting quantum entanglement and quantum squeezing. This field promises to develop measurement techniques that give better precision than the ...
Fisher information metric. In information geometry, the Fisher information metric[1] is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures defined on a common probability space. It can be used to calculate the informational difference between ...